title: Iron Fist (season 2)

text: When asked how the season would be influenced by the criticisms of the first, Metzner said that Marvel had allowed him to tell his own story rather than follow on from the first season and so he just approached the project as a fan of the comics and characters. He described the second season as an "evolution" of the first. Jones felt that Rand would be more relatable for the audience in the second season after moving in with his girlfriend and spending less time around Rand Enterprises. Metzner described this approach as "holistic", wanting the series to feel like being on the streets of New York.


title: Iron Fist (season 2)

text: Finn Jones, Jessica Henwick, Tom Pelphrey, Jessica Stroup, and Sacha Dhawan reprise their roles as Danny Rand / Iron Fist, Colleen Wing, Ward Meachum, Joy Meachum, and Davos, respectively. They are joined in the season by Alice Eve as Typhoid Mary. Metzner had previously written a different version of Typhoid Mary for the film "Elektra" (2005), and was always interested in that character and well-versed in her comic story. Eve described her introduction in the season as an origin story that explores the mystery of the character's multiple personalities, while Loeb said, "We meet her at a certain point in her life and then cards get tipped over as you go."


title: Iron Fist (season 2)

text: With the announcement of the season, it was revealed that Simone Missick would appear, reprising her role as Misty Knight from previous MCU Netflix series. This allows for the exploration of the Daughters of the Dragon team that Wing and Knight form in the comics. James Chen had also joined the cast as Sam Chung, a role loosely based on the comics supporting character of the same name.


title: Iron Fist (season 2)

text: Filming for the season was expected to begin "soon" after it was announced at San Diego Comic-Con, with actor Sacha Dhawan saying then that "they're hopefully starting" by December 2017. By December 13, filming on the season had begun, in New York City where the production wrapped on May 10, 2018. Jones described this as the end of a "long and physical 7 month winter shoot". Extensive filming took place in New York's Chinatown. Niels Alpert served as cinematographer for the season.


title: Iron Fist (season 2)

text: Clayton Barber took over as the fight coordinator for the season, having also served in the role on Marvel's "Black Panther" (2018), after the fight choreography of the first season was widely criticized. Barber was inspired by "old school kung fu" such as the works of Jackie Chan, and wanted to make the fights of the series feel like "a punk rock song". Metzner noted that Jones had months of lead time before work on the season began to "hone his skills" with the fighting and stunts, and said that he and the rest of the cast along with Barber "really pushed themselves" with the fight sequences in the season. Jones added that all of the fight scenes have "an emotional standpoint" so that they drive the story forward rather than simply being "awesome fight scenes" for the sake of having fights.


title: Iron Fist (season 2)

text: The fictional country of Sokovia that was introduced in the MCU film "" (2015) is referenced in the season as part of Walker's past as an operative in the country.


title: Iron Fist (season 2)

text: Jones, Henwick, Missick, Eve, Loeb, Metzner, and Barber promoted the season at San Diego Comic-Con 2018. Charles Pulliam-Moore of io9 felt the footage shown at the panel left him optimistic for the season, since "It finally feels like "Iron Fist" may have figured out what people wanted out of this show in the first place." He felt the clips showed "how drastic an improvement" there was to the fight choreography, thanks in part to new fight coordinator Barber joining the series. One clip that showed Rand facing Davos in K'un-Lun felt "brutal and bloody" while also being "fluid and elegant in a way that feels fresh, new, and like what you want from "Iron Fist"." At the panel, Loeb appeared in a karate costume, as part of a comedic bit with Henwick, who later appeared on stage telling Loeb to remove the outfit. Some criticized the outfit as insensitive and "several layers of bad".


title: Iron Fist (season 2)

text: The second season of "Iron Fist", consisting of ten episodes, was released on September 7, 2018, on the streaming service Netflix worldwide, in Ultra HD 4K and high dynamic range. The season, along with the additional "Iron Fist" season and the other Marvel Netflix series, was removed from Netflix on March 1, 2022, due to Netflix's license for the series ending and Disney regaining the rights. The season became available on Disney+ in the United States, Canada, United Kingdom, Ireland, Australia, and New Zealand on March 16, ahead of its debut in Disney+'s other markets by the end of 2022.


title: Iron Fist (season 2)

text: The review aggregation website Rotten Tomatoes reported a 55% approval rating, based on 47 reviews, with an average rating of 5.70/10. The website's critical consensus reads, "Better action scenes and tighter pacing elevate "Iron Fist"s second season, but it remains a lesser light among MCU shows." Metacritic assigned a score of 39 out of 100 based on reviews from six critics, indicating "generally unfavorable reviews".


title: Battle of Franklin (1864)

text: The Second Battle of Franklin was fought on November 30, 1864, in Franklin, Tennessee, as part of the Franklin–Nashville Campaign of the American Civil War. It was one of the worst disasters of the war for the Confederate States Army. Confederate Lt. Gen. John Bell Hood's Army of Tennessee conducted numerous frontal assaults against fortified positions occupied by the Union forces under Maj. Gen. John Schofield and was unable to prevent Schofield from executing a planned, orderly withdrawal to Nashville.


title: Battle of Franklin (1864)

text: The Confederate assault of six infantry divisions containing eighteen brigades with 100 regiments numbering almost 20,000 men, sometimes called the "Pickett's Charge of the West", resulted in devastating losses to the men and the leadership of the Army of Tennessee—fourteen Confederate generals (six killed, seven wounded, and one captured) and 55 regimental commanders were casualties. After its defeat against Maj. Gen. George H. Thomas in the subsequent Battle of Nashville, the Army of Tennessee retreated with barely half the men with which it had begun the short offensive, and was effectively destroyed as a fighting force for the remainder of the war.


title: Battle of Franklin (1864)

text: The 1864 Battle of Franklin was the second military action in the vicinity; a battle in 1863 was a minor action associated with a reconnaissance in force by Confederate cavalry leader Maj. Gen. Earl Van Dorn on April 10.


title: Battle of Franklin (1864)

text: Following his defeat in the Atlanta Campaign, Hood had hoped to lure Maj. Gen. William T. Sherman into battle by disrupting his railroad supply line from Chattanooga to Atlanta. After a brief period in which he pursued Hood, Sherman decided instead to cut his main army off from these lines and "live off the land" in his famed March to the Sea from Atlanta to Savannah. By doing so, he would avoid having to defend hundreds of miles of supply lines against constant raids, through which he predicted he would lose "a thousand men monthly and gain no result" against Hood's army.


title: Battle of Franklin (1864)

text: Sherman's march left the aggressive Hood unoccupied, and his Army of Tennessee had several options in attacking Sherman or falling upon his rear lines. The task of defending Tennessee and the rearguard against Hood fell to Maj. Gen. George H. Thomas, commander of the Army of the Cumberland. The principal forces available in Middle Tennessee were IV Corps of the Army of the Cumberland, commanded by Maj. Gen. David S. Stanley, and XXIII Corps of the Army of the Ohio, commanded by Maj. Gen. John Schofield, with a total strength of about 30,000. Another 30,000 troops under Thomas's command were in or moving toward Nashville.


title: Battle of Franklin (1864)

text: Rather than trying to chase Sherman in Georgia, Hood decided that he would attempt a major offensive northward, even though his invading force of 39,000 would be outnumbered by the 60,000 Union troops in Tennessee. He would move north into Tennessee and try to defeat portions of Thomas's army in detail before they could concentrate, seize the important manufacturing and supply center of Nashville, and continue north into Kentucky, possibly as far as the Ohio River.


title: Battle of Franklin (1864)

text: Hood even expected to pick up 20,000 recruits from Tennessee and Kentucky in his path of victory and then join up with Robert E. Lee's army in Virginia, a plan that historian James M. McPherson describes as "scripted in never-never land." Hood had recovered from but was affected by a couple of serious physical battle wounds to a leg and arm, which caused him pain and limited his mobility. Hood spent the first three weeks of November quietly supplying the Army of Tennessee in northern Alabama in preparation for his offensive.


title: Battle of Franklin (1864)

text: The Army of Tennessee marched north from Florence, Alabama, on November 21, and indeed managed to surprise the Union forces, the two halves of which were apart at Pulaski, Tennessee and at Nashville. With a series of fast marches that covered in three days, Hood tried to maneuver between the two armies to destroy each in detail. But Union general Schofield, commanding Stanley's IV Corps as well as his own XXIII Corps, reacted correctly with a rapid retreat from Pulaski to Columbia, which held an important bridge over the Duck River on the turnpike north. Despite suffering losses from Maj. Gen. Nathan Bedford Forrest's cavalry along the way, the Federals were able to reach Columbia and erect fortifications just hours before the Confederates arrived on November 24. From November 24 to 29, Schofield managed to block Hood at this crossing, and the "Battle of Columbia" was a series of mostly bloodless skirmishes and artillery bombardments while both sides re-gathered their armies.


title: Battle of Franklin (1864)

text: On November 28, Thomas directed Schofield to begin preparations for a withdrawal north to Franklin. He was incorrectly expecting that Maj. Gen. A. J. Smith's XVI Corps arrival from Missouri was imminent and he wanted the combined force to defend against Hood on the line of the Harpeth River at Franklin instead of the Duck River at Columbia. Meanwhile, early on the morning of November 29, Hood sent Benjamin F. Cheatham's and Alexander P. Stewart's corps north on a flanking march. They crossed the Duck River at Davis's Ford east of Columbia, while two divisions of Stephen D. Lee's corps and most of the army's artillery remained on the southern bank to deceive Schofield into thinking a general assault was planned against Columbia.


title: Battle of Franklin (1864)

text: Now that Hood had outflanked him by noon on November 29, Schofield's army was in critical danger. His command was split at that time between his supply wagons and artillery and part of the IV Corps, which he had sent to Spring Hill nearly ten miles north of Columbia, and the rest of the IV and XXIII corps marching from Columbia to join them. In the Battle of Spring Hill that afternoon and night, Hood had a golden opportunity to intercept and destroy the Union troops and their supply wagons, as his forces had already reached the turnpike separating the Union forces by nightfall. However, because of a series of command failures along with Hood's premature confidence that he had trapped Schofield, the Confederates failed to stop or even inflict much damage to the Union forces during the night. Both the Union infantry and supply train managed to pass Spring Hill unscathed by dawn on November 30, and soon occupied the town of Franklin to the north. That morning, Hood was surprised and furious to discover Schofield's unexpected escape. After an angry conference with his subordinate commanders in which he blamed everyone but himself for the mistakes, Hood ordered his army to resume its pursuit north to Franklin.


title: Battle of Franklin (1864)

text: Schofield's advance guard arrived in Franklin at about 4:30 a.m. on November 30, after a forced march north from Spring Hill. Brig. Gen. Jacob Cox, commander of the 3rd Division, temporarily assumed command of the XXIII Corps and immediately began preparing strong defensive positions around the deteriorated entrenchments originally constructed for a previous engagement in 1863.


title: Battle of Franklin (1864)

text: Schofield decided to defend at Franklin with his back to the river because he had no pontoon bridges available that would enable his men to cross the river. The bridges had been left behind in his retreat from Columbia because they lacked wagons to transport them, and pontoons requested from Thomas in Nashville had not arrived. Schofield needed time to repair the permanent bridges spanning the river—a burned wagon bridge and an intact railroad bridge. He ordered his engineers to rebuild the wagon bridge and to lay planking over the undamaged railroad bridge to enable it to carry wagons and troops. His supply train parked in the side streets to keep the main pike open, while wagons continued to cross the river, first via a ford next to the burned-out pike bridge, and later in the afternoon by the two makeshift bridges. By the beginning of the assault, nearly all the supply wagons were across the Harpeth and on the road to Nashville.


title: Battle of Franklin (1864)

text: By noon, the Union works were ready. The line formed an approximate semicircle around the town from northwest to southeast. The other half of the circle was the Harpeth River. Counterclockwise from the northwest were the divisions of Kimball (IV Corps), Ruger (XXIII Corps), and Reilly (XXIII Corps). There was a gap in the line where the Columbia Pike (present day U.S. Route 31) entered the outskirts of the town, left open to allow passage of the wagons. About behind this gap, a 150-yard "retrenchment" line was constructed of dirt and rails, which was intended to be a barrier to traffic, not a full-fledged defensive earthwork. (The gap was also defended by the guns of Battery A, 1st Kentucky Artillery. The men of the 44th Missouri also extended the retrenchment line to the west along their front with hastily dug trenches.) The actual earthworks in the southern portion of the line were formidable. Attacking infantry would be confronted by a ditch about four feet wide and two to three feet deep, then a wall of earth and wooden fence rails four feet above normal ground level, and finally a trench three to four feet deep in which the defenders stood, aiming their weapons through narrow "head gaps" formed by logs. In the southeast portion of the line, Osage-orange shrubs formed an almost impenetrable abatis. Just behind the center of the line stood the Carter House, appropriated as Cox's headquarters. Just east of the pike was the Carter cotton gin building, around which a minor salient occurred in the Union earthworks. Schofield established his headquarters in the Alpheus Truett House, a half mile north of the Harpeth on the Nashville Pike, although he would spend most of his time during the battle in Fort Granger, built in 1863 as an artillery position northeast of the town.


title: Battle of Franklin (1864)

text: Two Union brigades were positioned about a half mile forward of the main line. George D. Wagner's division had been the last to arrive from Spring Hill, and after briefly stopping at Winstead Hill before Hood arrived, he ordered his brigades under Colonels Emerson Opdycke, John Q. Lane, and Joseph Conrad (who had replaced Luther Bradley, wounded at Spring Hill) to stop halfway to the Union line and dig in as best they could on the flat ground. Stanley had earlier ordered Wagner to hold Winstead Hill until dark unless he was pressed, and it is possible that Wagner somehow translated these orders into the notion that he was supposed to hold a line south of the main position. Opdycke considered Wagner's order to be ridiculous and refused to obey it; he marched his brigade through the Union line and into a reserve position behind the gap through which the Columbia Pike passed. (A few days after his ill-considered position was overrun in the Confederate advance, Wagner was relieved of command at his own request.)


title: Battle of Franklin (1864)

text: Wood's division of IV Corps and all of Wilson's cavalry were posted north of the Harpeth to watch for any flanking attempt. Schofield planned to withdraw his infantry across the river by 6:00 p.m. if Hood had not arrived by then. As Hood approached, Schofield initially assumed the Confederates were demonstrating as they had at Columbia, planning to cross the Harpeth and turn the Union position. He did not suspect that Hood would be rash enough to attack the strong defensive line.


title: Battle of Franklin (1864)

text: Hood's army began to arrive on Winstead Hill, two miles (3 km) south of Franklin, around 1:00 p.m. Hood ordered a frontal assault in the dwindling afternoon light—sunset would be at 4:34 p.m. that day—against the Union force, a decision that caused dismay among his top generals. Forrest argued unsuccessfully that if he were given a division of infantry to accompany his cavalry, he could flank Schofield out of his position "within an hour." Frank Cheatham told Hood, "I do not like the looks of this fight; the enemy has an excellent position and is well fortified." But Hood countered that he would rather fight a Federal force that had had only a few hours to build defenses, instead of Nashville where "they have been strengthening themselves for three years." Patrick Cleburne observed the enemy fortifications as being formidable, but he told the commanding general that he would either take the enemy's works or fall in the attempt. He later remarked to Brig. Gen. Daniel C. Govan, "Well, Govan, if we are to die, let us die like men."


title: Battle of Franklin (1864)

text: Some popular histories assert that Hood acted rashly in a fit of rage, resentful that the Federal army had slipped past his troops the night before at Spring Hill and that he wanted to discipline his army by ordering them to assault against strong odds. Recent scholarship discounts this as unlikely, as it was not only militarily foolish, but Hood was observed to be determined, not angry, by the time he arrived in Franklin.


title: Battle of Franklin (1864)

text: Regardless of Hood's personal motivations, his specific objective was to try to crush Schofield before he and his troops could escape to Nashville. He was concerned that if he attempted to turn Schofield by crossing the Harpeth and getting between him and Nashville, the maneuver would be time-consuming and the open terrain of the area would reveal his movements prematurely, causing Schofield to simply withdraw again. The Confederates began moving forward at 4:00 p.m., with Cheatham's corps on the left of the assault and Stewart's on the right. Bate's division, on the left, was delayed in reaching its starting point as it marched around Winstead Hill, a movement that delayed the start of the entire army. Hood divided Forrest's cavalry—Chalmer's division on the far left, beyond Bate, and Buford and Jackson with Forrest, covering Stewart and facing the fords on the Harpeth. Lee's corps, and almost all of the army's artillery, had not yet arrived from Columbia. Hood's attacking force, about 19–20,000 men, was arguably understrength for the mission he assigned—traversing two miles (3 km) of open ground with only two batteries of artillery support and then assaulting prepared fortifications.


title: Battle of Franklin (1864)

text: Maj. Gen. John M. Schofield, commander of the Army of the Ohio, led a force of about 27,000 consisting of:


title: Battle of Franklin (1864)

text: Lt. Gen. John Bell Hood's Army of Tennessee, at 39,000 men, constituted the second-largest remaining army of the Confederacy, ranking in strength only after Gen. Robert E. Lee's Army of Northern Virginia. The army consisted of the corps of:


title: Battle of Franklin (1864)

text: At Franklin, about 27,000 Confederates were engaged, primarily from the corps of Cheatham, Stewart, and Forrest, and Johnson's division of Lee's corps.


title: Battle of Franklin (1864)

text: Hood's attack initially enveloped the 3,000 men in two brigades under Lane and Conrad, which attempted to stand their ground behind inadequate fieldworks and without anchored flanks, but quickly collapsed under the pressure. As Wagner exhorted his men to stand fast, they let loose a single strong volley of rifle fire, and a two-gun section of Battery G, 1st Ohio Light Artillery, fired canister, but then many of the veteran soldiers of the two brigades stampeded back on the Columbia Pike to the main breastworks, while some untried replacements were reluctant to move under fire and were captured. Nearly 700 of Wagner's men were taken prisoner. The fleeing troops were closely pursued by the Confederates, and a cry was repeated along the line, "Go into the works with them." The pursued and pursuers were so intermingled that defenders in the breastworks had to hold their fire to avoid hitting their comrades.


title: Battle of Franklin (1864)

text: The Union's momentary inability to defend the opening in the works caused a weak spot in its line at the Columbia Pike from the Carter House to the cotton gin. The Confederate divisions of Cleburne, Brown, and French converged on this front and a number of their troops broke through the now not-so-solid Federal defenses on either side. The 100th Ohio Infantry, of Reilly's brigade, was driven back from its position to the east of the pike and Col. Silas A. Strickland's brigade (Ruger's division) was forced to withdraw back to the Carter House. The left wing of the 72nd Illinois Infantry was swept away and rallied on the 183rd Ohio Infantry, in reserve at the retrenchment, which prompted the remainder of the 72nd to withdraw back to that line. In a matter of minutes, the Confederates had penetrated 50 yards deep into the center of the Federal line.


title: Battle of Franklin (1864)

text: As the Confederates poured men into the breach, Emerson Opdycke's brigade was in reserve, positioned in columns of regiments facing north in a meadow about 200 yards north of the Carter House. Opdycke quickly repositioned his men into line of battle, straddling the road, and they were confronted by masses of fleeing Union soldiers, pursued by Confederates. Opdycke ordered his brigade forward to the works. At the same time, his corps commander, David Stanley, arrived on the scene. He later wrote, "I saw Opdycke near the center of his line urging his men forward. I gave the Colonel no orders as I saw him engaged in doing the very thing to save us, to get possession of our line again." As he rode forward, Stanley had his horse shot out from under him and a bullet passed through the back of his neck, putting him temporarily out of action.


title: Battle of Franklin (1864)

text: Opdycke's counterattack was joined by reserve elements of Reilly's division (the 12th Kentucky Infantry and 16th Kentucky Infantry) and survivors of Strickland's and Wagner's divisions. Together they sealed the breach. Hand-to-hand fighting around the Carter House and the pike was furious and desperate, employing such weapons as bayonets, rifle butts, entrenching tools, axes, and picks.


title: Battle of Franklin (1864)

text: Firing continued around the Carter house and gardens for hours. Many in Brown's division were driven back to the Federal earthworks, where many were pinned down for the remainder of the evening, unable to either advance or flee. Each side fired through embrasures or over the top of the parapets at close range in an attempt to dislodge the other. Brown's division suffered significant losses, including Brown, who was wounded, and all four of his brigade commanders were casualties. Brown's brigade under Brig. Gen. George W. Gordon had angled to the right during the advance, joining Cleburne's division to the east of the pike. Their attack near the cotton gin was driven back from the breastworks and was then subjected to devastating cross fire from Reilly's brigade to their front and the brigade of Col. John S. Casement, on Reilly's right. Cleburne was killed in the attack and 14 of his brigade and regimental commanders were casualties.


title: Battle of Franklin (1864)

text: That some Union troops were armed with Spencer and Henry repeating rifles added to the otherwise considerable advantages of the defenders. Near the Carter House, 350 men of the 12th Kentucky and 65th Illinois fired 16-shot, lever-action Henry rifles, the predecessors to the Winchester repeating rifle. These rifles, capable of at least 10 shots per minute, gave these men several times more firepower than typical infantrymen with the more common muzzle-loading rifle-muskets.


title: Battle of Franklin (1864)

text: While fighting raged at the center of the Union line, the Confederates of Stewart's corps also advanced against the Union left. Because the Harpeth River flowed in that area from southeast to northwest, the brigade found itself moving through a space getting progressively narrower, squeezing brigades together into a compressed front, delaying their movements and reducing their unit cohesion. Walthall's division was pressured so much from the right that it temporarily fell in front of Cleburne's advance. They were all subjected to fierce artillery fire not only from the main Union line, but also from the batteries across the river at Fort Granger. They also had significant difficulty pushing through the strong osage-orange abatis.


title: Battle of Franklin (1864)

text: Loring's division launched two attacks against the Union brigade of Col. Israel N. Stiles and both were repulsed with heavy losses. Artillery firing canister rounds directly down the railroad cut prevented any attempt to flank the Union position. Brig. Gen. John Adams attempted to rally his brigade by galloping his horse directly onto the earthworks. As he attempted to seize the flag of the 65th Illinois, he and his horse were both shot and killed. The brigade of Brig. Gen. Winfield S. Featherston began falling back under heavy fire when its division commander, Maj. Gen. William W. Loring, confronted them, shouting, "Great God. Do I command cowards?" He attempted to inspire his men by sitting on his horse in full view of the Federal lines for over a minute and amazingly emerged unharmed, but the brigade made no further progress.


title: Battle of Franklin (1864)

text: Walthall's division, intermixed partially with Loring's division because of the confusion that resulted from the narrow space, struck Casement's and Reilly's brigades in multiple waves of brigade assaults—probably as many as six distinct attacks. All of these assaults were turned back with heavy losses. The brigade of Brig. Gen. William A. Quarles was able to push through the abatis and reached the Federal earthworks, where it was pinned down by murderous crossfire. Quarles was wounded in the left arm and at the end of the battle the highest-ranking officer standing in his brigade was a captain.


title: Battle of Franklin (1864)

text: Maj. Gen. William B. Bate's division had a long distance to march to reach its assigned objective on the Union right and when he gave the final order to attack it was almost dark. First contact with the enemy came around the Everbright Mansion, the home of Rebecca Bostick, and the Confederates pushed aside Union sharpshooters and swept past the house. However, Bate's left flank was not being protected as he expected by Chalmers's cavalry division, and they received enfilade fire. To protect the flank, Bate ordered the Florida Brigade, temporarily commanded by Col. Robert Bullock, to move from its reserve position to his left flank. This not only delayed the advance, but provided only a single line to attack the Union fortifications, leaving no reserve. Chalmers's troopers had actually engaged the Federal right by this time (the brigades of Col. Isaac M. Kirby and Brig. Gen. Walter C. Whitaker of Kimball's division), fighting dismounted, but Bate was unaware of it because the two forces were separated by rolling ground and orchards. Neither Bate nor Chalmers made any progress and they withdrew.


title: Battle of Franklin (1864)

text: Hood, who remained at his headquarters on Winstead Hill, was still convinced that he could pierce the Federal line. At about 7 p.m., he deployed the only division of Stephen D. Lee's corps that had arrived, commanded by Maj. Gen. Edward "Allegheny" Johnson, to assist Cheatham's effort. They moved north on the west side of the Columbia Turnpike and passed around Privet Knob, Cheatham's headquarters, but were unfamiliar with the terrain in the dark and Cheatham told Lee he had no staff officer left who could guide them. Both Bate and Cheatham warned Lee not to fire indiscriminately against the Federal works because Confederates were pinned down there on the outside. Johnson's men lost their unit alignments in the dark and had significant difficulties attacking the works just to the west of the Carter House. They were repulsed after a single assault with heavy losses.


title: Battle of Franklin (1864)

text: In addition to Chalmers's actions in the west, across the river to the east Confederate cavalry commander Forrest attempted to turn the Union left. His two divisions on Stewart's right (Brig. Gens. Abraham Buford II and William H. Jackson) engaged some Federal cavalry pickets and pushed them back. They crossed the Harpeth at Hughes Ford, about upstream from Franklin. When Union cavalry commander Brig. Gen. James H. Wilson learned at 3 p.m. that Forrest was crossing the river, he ordered his division under Brig. Gen. Edward Hatch to move south from his position on the Brentwood Turnpike and attack Forrest from the front. He ordered Brig. Gen. John T. Croxton's brigade to move against Forrest's flank and held Col. Thomas J. Harrison's brigade in reserve. The dismounted cavalrymen of Hatch's division charged the Confederate cavalrymen, also dismounted, and drove them back across the river. Some of Croxton's men were armed with seven-shot Spencer carbines, which had a devastating effect on the Confederate line. Wilson was proud of his men's accomplishment because this was the first time that Forrest had been defeated by a smaller force in a standup fight during the war.


title: Battle of Franklin (1864)

text: Following the failure of Johnson's assault, Hood decided to end offensive actions for the evening and began to plan for a resumed series of attacks in the morning. Schofield ordered his infantry to cross the river, starting at 11 p.m., despite objections from Cox that withdrawal was no longer necessary and that Hood was weakened and should be counter-attacked. Schofield had received orders from Thomas to evacuate earlier that day—before Hood's attack began—and he was happy to take advantage of them despite the changed circumstances. Although there was a period in which the Union army was vulnerable, outside its works and straddling the river, Hood did not attempt to take advantage of it during the night. The Union army began entering the breastworks at Nashville at noon on December 1, with Hood's damaged army in pursuit.


title: Battle of Franklin (1864)

text: The damaged Confederate force was left in control of Franklin, but its enemy had escaped again. Although he had briefly come close to breaking through in the vicinity of the Columbia Turnpike, Hood was unable to destroy Schofield or prevent his withdrawal to link up with Thomas in Nashville. And his unsuccessful result came with a frightful cost. The Confederates suffered 6,252 casualties, including 1,750 killed and 3,800 wounded. An estimated 2,000 others suffered less serious wounds and returned to duty before the Battle of Nashville. But more importantly, the military leadership in the West was decimated, including the loss of perhaps the best division commander of either side, Patrick Cleburne, who was killed in action. Fourteen Confederate generals (six killed, seven wounded, and one captured) and 55 regimental commanders were casualties. Five generals killed in action at Franklin were Cleburne, John Adams, Hiram B. Granbury, States Rights Gist, and Otho F. Strahl. A sixth general, John C. Carter, was mortally wounded and died later on December 10. The wounded generals were John C. Brown, Francis M. Cockrell, Zachariah C. Deas, Arthur M. Manigault, Thomas M. Scott, and Jacob H. Sharp. One general, Brig. Gen. George W. Gordon, was captured. Also among the dead was Tod Carter, the middle child of the Carter family. Having enlisted in the Confederate army three years earlier, Carter had returned to his hometown for the first time since then, only to be wounded in battle just a few hundred yards away from his own house. He was found by his family after the battle, and died early in the next day.


title: Battle of Franklin (1864)

text: Union losses were reported as only 189 killed, 1,033 wounded, and 1,104 missing. It is possible that the number of casualties was under-reported by Schofield because of the confusion during his army's hasty nighttime evacuation of Franklin. The Union wounded were left behind in Franklin. Many of the prisoners, including all captured wounded and medical personnel, were recovered on December 18 when Union forces re-entered Franklin in pursuit of Hood.


title: Battle of Franklin (1864)

text: The Army of Tennessee was badly damaged at Franklin. Nevertheless, rather than retreat and risk the army dissolving through desertions, Hood advanced his 26,500 man force against the Union army now combined under Thomas, firmly entrenched at Nashville which numbered more than 60,000. Hood and his department commander Gen. P.G.T. Beauregard requested reinforcements, but none were available. Strongly outnumbered and exposed to the elements, Hood was attacked by Thomas on December 15–16 at the Battle of Nashville, defeated decisively and pursued aggressively, retreating to Mississippi with just under 20,000 men. The Army of Tennessee never fought again as an effective force and Hood's career was ruined.


title: Battle of Franklin (1864)

text: Perhaps surprisingly, some Confederate soldiers claimed that Franklin was a victory. James Lanning of the 25th Alabama Infantry wrote in his diary, “victory is ours but very dearly bought.” Confederate artilleryman William Ritter believed, “the charge was a brilliant one and was successful, as part of the enemy’s line was captured.” Joseph Boyce of the 1st Missouri Infantry acknowledged that many men considered Franklin a victory for the Confederate army since it held the battlefield at the end of the fighting. However Boyce, who was wounded at Franklin, also noted “two such victories will wipe out any army.”


title: Battle of Franklin (1864)

text: Hood's continued pursuit of Schofield after suffering defeat at Franklin and his refusal to withdraw before the battle of Nashville caused Schofield to remark "I doubt if any soldiers in the world ever needed more cumulative evidence to convince them that they were beaten."


title: Battle of Franklin (1864)

text: In his Pulitzer Prize-winning book "Battle Cry of Freedom", James M. McPherson wrote, "Having proved even to Hood's satisfaction that they could assault breastworks, the Army of Tennessee had shattered itself beyond the possibility of ever doing so again. David J. Eicher wrote that Hood "had in effect mortally wounded his army at Franklin."


title: Battle of Franklin (1864)

text: The Carter House, which stands today and is open to visitors, was located at the center of the Union position. The site covers about . The house and outbuildings still show hundreds of bullet holes. The Carnton Plantation, home to the McGavock family during the battle, also still stands and is likewise open to the public. The Carnton Plantation home was one of 44 Franklin homes serving as a hospital, often with 30 wounded in each small room of the house. Confederate soldiers of Stewart's Corps swept past Carnton toward the left wing of the Union army and the house and outbuildings were converted into the largest field hospital present after the battle. Adjacent to Carnton is the McGavock Confederate Cemetery, where 1,481 Southern soldiers killed in the battle are buried. Adjacent to the surrounding Carnton is another of battlefield, formerly the Franklin Country Club golf course, which is currently being converted to a city park.


title: Battle of Franklin (1864)

text: Much of the rest of the Franklin battlefield has been lost to commercial development. The spot where Gen. Cleburne fell, for instance, was covered until late 2005 by a Pizza Hut restaurant. City officials and historic-preservation groups have recently placed a new emphasis on saving what remains of the land over which the battle raged.


title: Battle of Franklin (1864)

text: In 2006, of land bordering the southwestern end of the Carter House property was acquired with help of the American Battlefield Trust and local organizations. This land was part of that made up the Carter Family Garden, which during the battle saw tremendous fighting and was part of a brief Confederate breakthrough. After the purchase, a house, out-buildings, and a swimming pool were removed. During excavation of the original Federal entrenchments some human bones were found.


title: Battle of Franklin (1864)

text: Starting in 2005, the area around the intersection of Columbia Ave. and Cleburne St. has seen a serious renewed effort to reclaim that area to be the heart of a future battlefield park. The location of the former Pizza Hut is now the home to Cleburne Park. The property where the Carter Cotton Gin was located during the battle was purchased in 2005. In 2008 the property behind this location and where the Federal line crossed Columbia Ave. was purchased and in May 2010 the property east of the Gin location and where part of the Gin may have stood was also purchased. All these locations have houses on them that will be either sold and moved or torn down. Preservation organizations plan to reconstruct both the Carter Cotton Gin and some of the Federal entrenchments.


title: Battle of Franklin (1864)

text: On November 24, 2010, the State of Tennessee awarded a $960,000 enhancement grant from the Tennessee Department of Transportation to help purchase the property where the Domino's Pizza and mini-mart is located. A local preservation organization is also hoping to purchase 16 acres of land in two parcels: five acres located southwest of what is now a small park called the Collin's Farm located at the southeast corner of the Lewisburg Pike and the Nashville and Decatur Railroad that was preserved a few years ago; and 11 acres located near the corner of Lewisburg Pike and Carnton Lane. The American Battlefield Trust and its federal, state and local partners have acquired and preserved a total of of the battlefield in more than 10 different transactions since 1996.


title: Battle of Franklin (1864)

text: In the book "Gone with the Wind" by Margaret Mitchell, the character Rhett Butler mentions that he fought at Franklin.


title: Top Gear test track

text: The "Top Gear" test track is used by the BBC automotive television programme "Top Gear". It is located at Dunsfold Aerodrome in Surrey, United Kingdom. The track was designed by Lotus Cars as a testing facility, with many of its Formula One cars tested there. It is used to test both cars and drivers seen on the programme, mainly in "Power Laps" and "Star in a ... Car".


title: Top Gear test track

text: For the 23rd series of "Top Gear" the track was expanded with a rallycross section for the "Star in a Rallycross Car" segment, but it was abandoned at the end of series 23.


title: Top Gear test track

text: In December 2016 planning permission was granted for 1,800 homes to be built on the current site of the aerodrome. As part of the redevelopment, it was proposed that the track (and associated aerodrome infrastructure such as the runway drag strip) was to be demolished.


title: Top Gear test track

text: The track is on a former Royal Canadian Air Force airbase constructed during the Second World War and later used by British Aerospace (and its predecessors) as a manufacturing and test facility. The track's main route, marked by painted lines and simple structures such as stacks of tyres, was designed by test drivers from Lotus. The layout of the track is designed to put the car through various conditions, ranging from provoking understeer to testing brake balance and tyres. The track is approximately long. It is considered to be an equaliser for cars since, according to Richard Hammond, both 0–60 miles per hour (0–96.6 km/h) times and top speed are totally meaningless. The track also incorporates a drag strip; although this is not used for timed segments, it does feature in some challenges and other features on the show.


title: Top Gear test track

text: The course starts on the perimeter road outside the "Top Gear" studio. The first bend is a fast right-left kink named "Crooner Curves." "Willson Bend" is the first proper turn on the track and the first corner usually seen when The Stig is lapping a car. "Chicago", a long right-hand around a tyre wall onto the main runway, was designed by Lotus as a steady state corner, designed to highlight understeer or oversteer of the chassis. Next is "Hammerhead", a left-then-right corner, which again highlights understeer and oversteer. The track comes to a right-hand curve, then the course turns right through the flat-out section called the "Follow Through" (it resembles turns 11 and 12 of the Albert Park Circuit). After the left hand "Bentley Bend" named after the person who first "discovered" Jeremy Clarkson and former "Top Gear" presenter, Jon Bentley, but commonly referred to simply as "the tyres", the course comes to "Bacharach Bend", which, after the first series, has been referred to as the "Penultimate Corner" or the "Second-to-last Corner" and is often regarded as one of the most challenging on the course. The final turn before the finish line is "Gambon" in honour of Sir Michael Gambon, who completed the turn on two wheels in episode 8 of Series 1. Prior to this, the corner was known as "Carpenters Corner".


title: Top Gear test track

text: The track is used routinely for the "Star in a Reasonably-Priced Car" and "Power Laps" segments on "Top Gear". It also serves myriad roles in other portions of the programme, especially in testing cars and in challenges. When testing cars, they are often driven around the airfield by the presenters. Afterwards, they are taken around the test track by The Stig to set a lap time. Occasionally, drag races and speed tests are held on the runway.


title: Top Gear test track

text: Cars acquired during challenges must often post lap times (driven by either one of the presenters or The Stig) around the track against either a target time or a time set by The Stig in another vehicle. During many challenges, the track is used in more unorthodox fashions — for instance, serving as a makeshift motorway lane during a challenge testing tailgating prowess with vans.


title: Top Gear test track

text: Power Laps is a segment of the programme in which The Stig completes a lap around the track in a reviewed car to compare its performance to previous contenders.


title: Top Gear test track

text: To be eligible to appear on the Power Lap Times board, a vehicle must be a road-legal production car and must have sufficient ride height to clear a standard speed bump (referred to by the presenters as a sleeping policeman), although occasionally vehicles that do not qualify to appear on the list are still timed. Whenever a non-qualifying vehicle is raced, the time is compared to the official Power Laps but then removed from the board, for example—the Ferrari FXX owned by Michael Schumacher (1:10.7) was taken off the board after because it both failed to meet road legal standards and used slick tyres.


title: Top Gear test track

text: All laps are timed with the car's manufacturer-provided adjustable settings configured for maximum performance—all adjustable suspensions are set at their most efficient, all gear shift maps are at their most aggressive, and driving aids such as traction control are deactivated. Lap times do not offer complete comparisons between the cars, mainly because wet or otherwise poor weather conditions (see "time deductions" below) can negatively affect lap times.


title: Top Gear test track

text: Due to the size of the list, only the top 20 are shown. See List of "Top Gear" test track Power Lap Times for the full list.


title: Top Gear test track

text: The second most powerful production car ever featured on "Top Gear", the 1001 PS (987 bhp; 736 kW) Bugatti Veyron, was taken around the track by The Stig in Series 12, Episode 4, after 3 years of waiting. However, it disappointed the team by only managing fifth place on the Power Board (currently 26th), an unexpectedly low position ultimately attributed to the car's kerb weight of , more than any of the four faster cars. In Series 15 Episode 5 however, the Stig took the 1,200 PS Super Sport version around the track in 1:16.8, thus setting a new lap record.


title: Top Gear test track

text: For the 1:17.6 lap, the Koenigsegg CCX (written as "Koeniggggsenisseggsegnignigsegigisegccx2 with the Top Gear wing" on a much-longer magnetic strip, because the presenters pretended not to be able to spell Koenigsegg) was fitted with an optional rear spoiler to provide downforce after The Stig spun the unmodified version off the track. The Stig allegedly recommended this modification, correctly predicting that the car would then be the fastest ever round the track, although Koenigsegg stated that the improvement was due to other adjustments.


title: Top Gear test track

text: A "non-qualifying" vehicle is one that does not meet the presenters' requirements to remain on the board; that is, one that is not a "road car", which according to "Top Gear" means being: available to buy, fully road-legal (lights, indicators, registration, profile tyres, etc.), and street-worthy (i.e. able to negotiate a speed bump).


title: Top Gear test track

text: The Caparo, Radical, and Westfield are road-legal in the UK but are unable to clear a speed bump. According to Caparo, the car driven by "Top Gear" was a prototype that did not feature the adjustable ride height found on the production model. Because The Stig set his time in the non-adjustable prototype and the production version has not been driven around the track, the Caparo's time remains ineligible for the Power Lap board.


title: Top Gear test track

text: Occasionally attempts at the Power Lap record are made without the support of the BBC. The following laps of Dunsfold were recorded, filmed and promoted independently of the "Top Gear" television programme.


title: Top Gear test track

text: Ultima say that their motive for running a non-televised lap was that they felt that the GTR was being specifically ignored by the producers of "Top Gear".


title: Top Gear test track

text: "Star in a Reasonably Priced Car" was a recurring segment on "Top Gear". During most programmes, a celebrity (usually, but not exclusively of British fame) is interviewed by Jeremy Clarkson. Discussion is normally amusing, and focuses on car-related matters, such as the celebrity's car history. Then Clarkson and the studio audience watch the guest's fastest lap on the "Top Gear" test track, after which Clarkson puts the celebrity's time on the time board.


title: Top Gear test track

text: For the first seven series the car driven for lap times was a Suzuki Liana. When first introduced, the car was worth £9995. The car used is stock except for a roll cage and racing seats added as safety measures. Each guest practises with The Stig before making several attempts to complete the test track in the fastest time. The guest does not learn their time until the interview. Practice laps, crashes and the drivers' facial expressions are also shown during the segment.


title: Top Gear test track

text: The two slowest laps on the Liana celebrity list are held by Terry Wogan and Richard Whiteley, both of whom were beaten by Billy Baxter, a blind Bosnian war veteran. He guided the Liana through the track under direction from Clarkson in the passenger seat in a time of 2 minutes 2 seconds, which was 1.4 seconds quicker than Terry Wogan, and 4 seconds faster than Richard Whiteley.


title: Top Gear test track

text: The fastest non-professional driver was Ellen MacArthur. Unlike most contenders she made no comments to the camera during her lap. She completed the lap in 1 minute 46.7 seconds, beating Jimmy Carr by 0.2 seconds. The current fastest professional driver in the Liana is Daniel Ricciardo with 1:42.2.


title: Top Gear test track

text: The Liana endured considerable abuse from the stars while undertaking their laps. In one incident, actor Michael Gambon clipped the final corner, taking the car onto two wheels. It was done in such a spectacular fashion that the corner was named "Gambon Corner". When Lionel Richie drove the Liana, one of the front wheels fell off, invoking Clarkson to coin the term "pulling a Lionel". Trevor Eve also lost a wheel. The former British transport minister Stephen Ladyman added further injury to the Liana by denting the boot when he lost control during practice and slid backwards into a tyre wall. David Soul destroyed the gearbox of two Lianas during his time on the show due to his rough driving style. Patrick Kielty broke the Liana's front suspension during series 4 when he drove on the grass. Christopher Eccleston was the only celebrity to use a Liana with an automatic transmission, because a hesitant Eccleston admitted he was "only qualified to drive an automatic." To accommodate his needs, "Top Gear" succeeded in borrowing an automatic Liana, of which only 40 existed in the UK. As a reference to his role in "Doctor Who", the automatic Liana was shown materialising onto the racing track, with a TARDIS materialisation sound effect played over it.


title: Top Gear test track

text: The Liana has also been modified on several occasions. David Soul's Liana featured a red police light and a white stripe in reference to his "Starsky and Hutch" role. Johnny Vegas was provided with L-plates as he had not passed his driving test at the time. When Justin Hawkins came on the show, the Liana he drove had flame decals pasted on it. Actor Sanjeev Bhaskar had an ornate tissue box placed in the back, a homage to Indian drivers.


title: Top Gear test track

text: In its service, the Liana covered 1,600 laps of the circuit; went through 400 tyres; its brakes were changed 100 times; and it required six new clutches, two new hubs, driveshafts, wishbones, struts and gear linkages and a replacement wing mirror.


title: Top Gear test track

text: In July 2005, Formula One driver Damon Hill appeared on the show for the first time as the star. This was kept a surprise to the audience and the viewing public, and when Nigel Mansell came on the show, it was covered up in magazines and on the internet by saying that the Star in a Reasonably Priced Car would be Alan Titchmarsh. Since Mansell's appearance the Liana has remained in use as a vehicle reserved for Formula 1 drivers.


title: Top Gear test track

text: For some of the laps more than one person has been present in the car. This was the case for Clarkson's run when he had both Hammond and Jason Dawe in the car. Trinny and Susannah were both in the car for each other's runs. Denise Van Outen was in the car when Johnny Vaughan did his lap; Van Outen never did a lap driving the car. Clarkson was also present as a navigator for Billy Baxter's laps.


title: Top Gear test track

text: Starting with the eighth series the Liana was replaced by a Chevrolet Lacetti and a new blank scoreboard. The format was changed so that each star would have five practice laps, and then a final timed lap, with no allowance being given for mishaps.


title: Top Gear test track

text: As a starter for the new car and format, an open day was held for any celebrity who wanted to take part. Seven stars recorded times that day: James Hewitt (who Jeremy and Richard referred to as the 'Well Spoken Man' after failing to recognise him), comedians Alan Davies and Jimmy Carr, rock stars Rick Wakeman and Justin Hawkins, footballer Les Ferdinand, and actor Trevor Eve who topped the time at 1 minute 47.0 seconds. Jimmy Carr, who held second place in the Liana behind Ellen MacArthur, spun off while doing his timed lap and got the second slowest time ever around the track at 2 minutes, 8.91 seconds.


title: Top Gear test track

text: On 28 January 2007, Jamie Oliver posted a time of 1:47.70 in melted snow and standing water. Given the rivalry Oliver felt towards fellow celebrity chef, and the lapboard leader, Gordon Ramsay, Oliver asked that the 4-second allowance normally granted for wet laps be used to put him at the top of the leaderboard "just for a day".


title: Top Gear test track

text: Actress Billie Piper posted a time of 1:48.3 but was deemed by The Stig to have failed to complete a lap properly, as she failed to negotiate some corners. The Stig suggested a three-second time penalty, but after Clarkson consulted the audience, it was decided to let the time stand, which her "Doctor Who" co-star, David Tennant, tried to overturn on 23 December 2007 show, at the end of the following series. Clarkson remarked that if Tennant had worn a see through top (like Piper for her interview), he "would have been faster than Simon Cowell".


title: Top Gear test track

text: In the 11 November 2007 episode, Simon Cowell retook his status as the holder of the fastest lap with a time of 1:45.90. According to Clarkson, the cameramen said they had never seen such consistency in the practice laps. However, Cowell was knocked off the top spot in Series 11 by Jay Kay, who now holds the fastest time in the Lacetti, although Clarkson selected the fastest of Jay Kay's times rather than the last run, which was slower than Cowell's time, seemingly due to a dislike of Cowell (he claimed earlier in the episode that Cowell had been at the top of the leaderboard for too long). Had this not happened, Cowell would have been knocked off the top by "Grand Designs" host Kevin McCloud.


title: Top Gear test track

text: Clarkson has referred to the part of the board with times of 1:51 and over as the 'Thespian Zone' due to the propensity for classically trained actors to post slow times.


title: Top Gear test track

text: Series 11 featured a slight change to the format, with two 'Stars' per episode instead of the previous one (although there had been a couple of editions in previous series' with more than one guest). Each of the pair are professionally associated with their fellow guest, usually both either act in or present the same TV show. Unlike previous episodes where two stars have appeared, the stars drove individual laps without the other present in the car.


title: Top Gear test track

text: On 28 March 2010, Richard Hammond attended the demolition of the two 550 ft chimneys at Lafarge Cement's Northfleet Works. On the first episode of Series 15, it was shown that the Lacetti was partially crushed by placing it in the path of one of the falling chimneys.


title: Top Gear test track

text: In the last episode of the fourteenth series of the show, Clarkson revealed that they were thinking about getting a new Reasonably Priced Car for the next series. On 27 June, during the first episode of the fifteenth series, it was revealed to be the Kia Cee'd and, as with the Chevrolet Lacetti, another open day was held to welcome the new car. Nick Robinson, Peter Jones, Al Murray, Bill Bailey, Peta Todd, Louie Spence, Johnny Vaughan and Amy Williams were among the initial drivers. Clarkson commonly refers to the Kia phonetically as the "Cee-apostrophe-d". Sophie Raworth, Bill Turnbull and Fiona Bruce all did the Star in a Reasonably Priced Car for Children in Need 2012.


title: Top Gear test track

text: In the first episode of series 20, Clarkson, Hammond and May revealed their new Reasonably Priced Car: a Vauxhall Astra 1.6 Tech Line. In similar fashion to earlier "new starts", an open day was held for multiple stars to drive the car. Following the abrupt end of Series 22 as a result of Clarkson's dismissal from the show, the Astra was returned to Vauxhall before being auctioned off for charity on 27 December 2015 for £17,800.


title: Top Gear test track

text: All Formula One drivers are put into their own list with regard to lap times because of their exceptional skill level. When the Liana was pulled out from retirement to allow Jenson Button to make a time, Clarkson noted that the Liana would be pulled out for use by Formula 1 drivers in the future. The original 'black' Stig and the first 'white' Stig have done laps around the track in the Suzuki Liana. Both had their times removed from the leaderboard upon their departure.


title: Top Gear test track

text: The first Stig was Perry McCarthy, who once test drove for the Williams F1 team, and drove for the ill-fated Andrea Moda Formula One team. The second Stig was Ben Collins; in the first episode of Series 13 the Stig was "revealed" to be Michael Schumacher, although this was a joke in the vein of the rest of his appearance on the show.


title: Top Gear test track

text: On 6 July 2011, Sebastian Vettel managed to top the board with a time of 1:44.0. Vettel's lap was the first time someone taking a 'Formula One drivers' line through the first corner was able to top The Stig's time, as Rubens Barrichello took the tighter line. Clarkson also mentioned on this episode that the current Stig has yet to do a lap of the track in the Liana, therefore there is currently no time on the board for the Stig. On 17 February 2013, Lewis Hamilton returned to do a dry lap and lowered the F1 Drivers record by 1.1s to 1:42.9. This was in the wake of his move to Mercedes AMG for the 2013 season. On 8 February 2015, Daniel Ricciardo topped the board with a lap time of 1:42.2. Ricciardo took the tighter line through the first corner, claiming that it covered less distance.


title: Top Gear test track

text: For series 23, "Star in a Reasonably Priced Car" was renamed as "Star in a Rally-Cross Car" segment, with the track expanded to include a "Rallycross" route, featuring the addition of a jump and a water splash obstacle, but retaining the use of some of the corners. Two celebrities were invited to partake in setting a fast lap time with the use of a Mini Rallycross Car. This segment was used only in this series, as following Chris Evans' resignation, it was scrapped due to negative feedback.


title: Top Gear test track

text: Starting from the twenty-fourth series, the basic format of "Star in a Reasonably Priced Car" was revived following the axing of the rally-cross format, though the name was changed to "Star in a Reasonably Fast Car" due to the use of a more powerful Toyota GT86. Both The Stig and Chris Harris instructing the celebrities on driving the car around the track. Footage of several celebrities who drove the car before the first episode of the twenty-fourth series, was aired on spin-off programme "Extra Gear".


title: Top Gear test track

text: On 24 October 2007, it was announced that players of the PlayStation 3 game, "Gran Turismo 5 Prologue", would be able to download episodes of "Top Gear" within the game, and that the test track would be one of the included circuits in the full game ("Gran Turismo 5").


title: Top Gear test track

text: A very basic yet driveable version of the track appeared around 2003 for the PC racing simulation "Grand Prix Legends". There is also a version of the test track for the realistic PC racing simulation "rFactor", produced with permission from Dunsfold park. The track has also been produced as an add-on for "World Racing 2". and the realistic racing simulator Assetto Corsa.


title: Top Gear test track

text: "Top Gear" have also added a basic version of the test track on the games section of their own website, with the title of "Be a star in our reasonably priced car". A "Top Gear" mobile phone game also features the track.


title: Top Gear test track

text: The game "Gran Turismo 5", developed by Polyphony Digital features a fully rendered version of the "Top Gear" track. Players have the ability to drive and race on the track.


title: Top Gear test track

text: The track also appeared in "Forza Motorsport 4"; the "Top Gear" logo appeared in a trailer for the game on the "Top Gear" website. Cars were shown racing in the follow-through section during the E3 2011 trailer. It is known that in the actual game there are options to race on the full track, race both of the rings in separate races and race on "Top Gear"s drag race mile. There is also an achievement for completing a lap of the "Top Gear" Test Track in the Kia Cee'd fittingly named "Star in a reasonably priced car".


title: Top Gear test track

text: "Forza Motorsport 4" sequel, "Forza Motorsport 5", also features the "Top Gear" test track. The track layouts from "Forza Motorsport 4" return, with the exception of the drag race mile, which has been removed. Subsequent games in the series, "Forza Motorsport 6" and "Forza Motorsport 7", also feature the "Top Gear" Test Track, with the full track and both separated rings. In these versions, the rings are able to be raced in reverse layout as well, and in both dry and wet conditions.


title: Top Gear test track

text: The track also appears in the mobile game "Top Gear – Extreme Parking", and in "Automation – The Car Company Tycoon Game" as "Airport Track" for players to test their cars on.


title: Darron Gibson

text: Darron Thomas Daniel Gibson (born 25 October 1987) is an Irish professional footballer who last played as a midfielder for League Two club Salford City, and formerly for the Republic of Ireland national team.


title: Darron Gibson

text: Born in Derry, Northern Ireland, he began his club career with Institute before joining Manchester United, for whom he made his professional debut in 2005. After loans with Belgium's Royal Antwerp and the Championship's Wolverhampton Wanderers, he won two League Cups, a Premier League title and the FIFA Club World Cup for United, totalling 60 games and 10 goals. In January 2012, he joined Everton for an undisclosed fee, where his appearances were limited from 2013 due to injury. He signed for Sunderland in January 2017, and left by mutual consent in March 2018. At the end of his professional career, he had spells with Wigan Athletic and Salford City, and appeared for Wythenshawe Amateurs in 2022.


title: Darron Gibson

text: In 2007, Gibson was at the centre of a dispute between the Football Association of Ireland (FAI) and the Irish Football Association (IFA), after he opted to play for the Republic of Ireland instead of Northern Ireland. The issue was referred to FIFA and was discussed in the Northern Ireland Assembly. The issue was settled in 2010 when it was declared that Northern Ireland-born people are entitled to play for either the Republic or Northern Ireland. Gibson represented the Republic of Ireland at UEFA Euro 2012.


title: Darron Gibson

text: Gibson was born in Derry, Northern Ireland. A former pupil of St Columb's College, he played junior football in the Derry and District League, and then with Institute before joining Manchester United in 2004. He made his senior debut for United on 26 October 2005 in a League Cup match against Barnet, coming on as a substitute for Lee Martin. During the 2005–06 season he played regularly for Manchester United Reserves, helping them win a treble. He made 19 appearances, scoring twice. In May 2006, he won the prestigious Jimmy Murphy Award as United's youth player of the year and then played regularly for the United senior team during their pre-season summer matches, together with Dong Fangzhuo, Jonny Evans, Fraizer Campbell and Danny Simpson.


title: Darron Gibson

text: Gibson was one of several United players who spent the 2006–07 season on loan at Royal Antwerp. In October 2007, he was loaned out again, this time to Wolverhampton Wanderers, where he spent the majority of the 2007–08 season. At Wolves he scored once, against Burnley on 8 December 2007.


title: Darron Gibson

text: Gibson made his Premier League debut on 15 November 2008, appearing as a second-half substitute against Stoke City, before making his UEFA Champions League debut ten days later, coming on as a substitute for Darren Fletcher against Villarreal on 25 November 2008. In December 2008, he travelled with the United squad to the 2008 FIFA Club World Cup in Japan, where, despite not making any appearances, he picked up a winners' medal. On 4 January 2009, Gibson scored his first goal for the club, United's third in a 3–0 victory over Southampton in the FA Cup third round. On 1 March 2009, Gibson started in the centre of midfield alongside Paul Scholes against Tottenham Hotspur in the 2009 League Cup Final at Wembley Stadium, playing the full initial 90 minutes before being replaced by Ryan Giggs at the start of extra time as Manchester United went on to win 4–1 on penalties. On 24 May, he scored his first league goal for Manchester United in the last match of the 2008–09 Premier League season against Hull City. Gibson was rewarded with a three-year extension to his Manchester United contract, tying him to the club until at least 2012.


title: Darron Gibson

text: Gibson was one of a number of young United players who came under criticism when they lost a four-year unbeaten home record in Europe, losing 1–0 to Beşiktaş at Old Trafford. On 1 December 2009, six days on from the defeat in the Champions League, Gibson responded to the criticism by scoring both of United's goals in a 2–0 win against Tottenham to send United through the semi-finals of the League Cup. Gibson was granted a starting place in the Champions League second leg quarter-final tie against Bayern Munich and scored a long-range shot after only three minutes, his first goal in a UEFA competition, but despite winning the match 3–2, they were knocked out by Bayern on away goals with the aggregate score ending 4–4.


title: Darron Gibson

text: He scored his first goal of the 2010–11 season as he netted the first of United's goals in a 5–2 away win over Scunthorpe United in the League Cup. In February 2011, Gibson's national team manager, Giovanni Trapattoni, told him that he must leave Manchester United in order to further his career. Gibson scored in the second leg of the Champions League semi-final as United beat Schalke 4–1 (6–1 on aggregate) but he was one of a number of players from that match alongside Rafael, Evans, O'Shea and Berbatov who could not make the substitutes bench for the Champions League final, which United lost 3–1 to Barcelona. Sunderland agreed a transfer fee with United to sign Gibson in the summer of 2011, but Gibson could not agree personal terms. He subsequently only made two appearances for the club in the 2011–12 season, despite there being a number of midfielders out injured at Old Trafford, and left the club in January 2012.


title: Darron Gibson

text: On 13 January 2012, Gibson signed for Everton for an undisclosed fee. He became the fourth ex-United player to sign for Everton under David Moyes, following Phil Neville, Tim Howard and Louis Saha. He made his debut a day later, as he started in a 1–1 draw with Aston Villa. Later that month, Gibson scored his first goal for the club in a 1–0 home win against league leaders Manchester City. Gibson played 11 times in the league during his first season with the club and did not finish on the losing side once. If his time at Manchester United is taken into account this figure is stretched to 28 consecutive league matches without defeat.


title: Darron Gibson

text: The run came to an end in Everton's third league match of the 2012–13 season, when Gibson started in a 0–2 loss to West Bromwich Albion, although the match was level at 0–0 when Gibson was substituted in the first half due to injury. Gibson was sent off for the first time in his career, in a 2–1 win away to West Ham United on 22 December 2012, although the red card and subsequent ban were rescinded by The Football Association five days later. On 13 April 2013, Gibson scored his first goal of the season in a 2–0 home win against Queens Park Rangers. His impact on Everton in his first two seasons was such that the club won 52% of the matches he played in and only 25% of those he did not, with Gibson being hailed as the key link between attack and defence.


title: Darron Gibson

text: Gibson only made one league appearance during the 2013–14 season as it was ended in October when he suffered serious cruciate knee ligament damage whilst on international duty.


title: Darron Gibson

text: On 8 November 2016, Gibson captained Everton's under-23 team in their elimination from the EFL Trophy by Blackpool.


title: Darron Gibson

text: Gibson signed for Sunderland, along with former Everton teammate Bryan Oviedo, in January 2017. He signed an 18-month deal for an undisclosed fee. He made his debut on 4 February as a 52nd-minute substitute for Jack Rodwell in a 4–0 win at Crystal Palace, and totalled 12 appearances as the Black Cats suffered relegation to the Championship.


title: Darron Gibson

text: After being charged with driving with excess alcohol in March 2018 Gibson was suspended by the club, before leaving by mutual consent less than a fortnight later.


title: Darron Gibson

text: On 3 August 2018, Wigan Athletic signed Gibson on a free transfer. He made his debut a day later, featuring in a 3–2 victory over Sheffield Wednesday. On 6 October, he was sent off in a 4–0 loss at Preston North End for a foul on Ben Pearson. He was released by Wigan at the end of the 2018–19 season.


title: Darron Gibson

text: Gibson signed a six-month contract with Salford City on 6 February 2020. He made his debut for the club on 19 February in a Football League Trophy semi-final victory over Newport County, playing the full match and scoring one of the penalties in the shoot-out. He was released by Salford on 17 May 2020 following the coronavirus enforced decision to end the League Two season, but subsequently rejoined the club ahead of the 2020–21 season; upon signing for the club for a second spell, his manager Graham Alexander said he was "delighted". On 17 October, Gibson suffered a broken leg in a match against Port Vale. At the end of the 2020–21 season, it was announced that he would be leaving the club.


title: Darron Gibson

text: Gibson was at the centre of a dispute between the Irish Football Association (IFA) and the Football Association of Ireland (FAI) over the eligibility of players born within Northern Ireland to represent the Republic of Ireland. The general principle or article 5 of FIFA's Regulations Governing the Application of the Statutes states that "any person holding a permanent nationality that is not dependent on residence in a certain country is eligible to play for the representative teams of the Association of that country". Due to the constitutional position of Northern Ireland following the signing of the Good Friday Agreement, citizenship of the Republic of Ireland is the undisputed birthright of every person born on the island of Ireland if they so wish, so long as at least one parent is an Irish or British citizen or, failing that, a permanent resident. As a result, Gibson was approached to represent both Northern Ireland and the Republic of Ireland at international level.


title: Darron Gibson

text: Gibson initially represented Northern Ireland at Under-16 level and was included in Victory Shield squads. However, he was dropped from the team after attending trials with Manchester United and subsequently switched allegiance to the Republic of Ireland. Before Gibson made his senior international debut for the Republic of Ireland, Nigel Worthington, the Northern Ireland manager, made an unsuccessful attempt to persuade him to switch his allegiance back.


title: Darron Gibson

text: Gibson first represented the Republic of Ireland at under-17 level. Then during the 2005–06 season he captained both the Republic of Ireland under-19 and under-21 squads. On 14 November 2006, he also played for Republic of Ireland B in a 0–0 draw against Scotland B. In 2007, Gibson was included in several senior Republic of Ireland squads for Euro 2008 qualifiers, before he eventually made his debut in a 4–0 win against Denmark. During the away friendly, he came on as half-time substitute, replacing Andy Reid. In the 54th minute, Gibson fired a shot from outside the penalty area that the Danish keeper, Jesper Christiansen, could only palm away, allowing Shane Long to follow up and score the Republic's third goal. Gibson won his second full cap on 8 September 2007 in an away match against Slovakia. The Euro 2008 qualifier, which finished as a 2–2 draw, saw him again used as substitute, this time replacing Aiden McGeady after 61 minutes.


title: Darron Gibson

text: Gibson made his first start for the Republic of Ireland national team in a 1–0 win at home to Cyprus on 15 October 2008. After Steven Reid dropped out of the Irish squad due to injury, Gibson was called up to provide extra physicality in the centre of the Irish midfield. Manager Giovanni Trapattoni also cited Gibson's confidence on the football pitch as the reason for choosing him ahead of Liam Miller and Andy Reid. On 8 February 2011, Gibson scored his first goal for his country, a shot from long range in a 3–0 victory over Wales in the first match of the 2011 Nations Cup.


title: Darron Gibson

text: Gibson was selected in the Ireland squad for UEFA Euro 2012. However, he was an unused substitute for all of Ireland's matches as the team was knocked out in the group stage with three successive defeats.


title: Darron Gibson

text: On 1 September 2012, Gibson was included in Ireland's squad to play Kazakhstan in a 2014 World Cup qualifier. However, he withdrew from the squad citing disappointment at his lack of playing time during Euro 2012. On 8 March 2013, he again turned down a call up for Ireland's World Cup qualifiers against Sweden and Austria.


title: Darron Gibson

text: On 30 September 2013, Gibson was recalled to the Republic of Ireland squad for the World Cup qualifiers against Germany and Kazakhstan by interim manager Noel King. After starting the 3–0 defeat to Germany he was stretchered off with a suspected knee injury in the next match against Kazakhstan which ruled him out for the rest of the season.


title: Darron Gibson

text: On 3 September 2014, Gibson made a start for the Republic of Ireland after recovering from his long term knee injury when his team beat Oman 2–0. On 11 October, he made his first competitive appearance for Ireland in more than a year, playing the full 90 minutes in the team's 7–0 UEFA Euro 2016 qualification defeat of Gibraltar.


title: Darron Gibson

text: In August 2015, Gibson was charged with driving without due care and attention, driving with excess alcohol and failing to stop after a road traffic collision in Altrincham, Greater Manchester. In September 2015 he admitted to drink driving, careless driving and failing to stop at the scene of an accident and was sentenced to a 12-month community order and banned from driving for 20 months.


title: Darron Gibson

text: In March 2018, Sunderland suspended Gibson after he was arrested on suspicion of driving over the legal alcohol limit, he was given a two-year community order and was banned from driving for 40 months, two months later after pleading guilty in court. The sentence was later reduced to a 27 month ban on appeal.


title: IU discography

text: South Korean singer-songwriter IU has released five studio albums, ten extended plays (EPs), 47 singles (including 19 as featured artist), five single albums, two remake albums and two compilation albums. In addition, the singer has collaborations and soundtracks for television series, films, and online games (including unreleased soundtracks).


title: IU discography

text: The singer debuted with "Lost Child" in September 2008, which was released as the lead single for her debut EP "Lost and Found" (2008). The single and the EP failed to enter the charts until 2012 and were considered a failure by the singer herself. The singers first studio album "Growing Up" was released in April 2009 and supported through three singles—"Boo", "You Know" and "Marshmallow". Between late-2008 and January 2010, there were no official South Korean charts. With the foundation of the Gaon Music Chart in February 2010, the album debuted on 85 on its first issued week and later peaked at no. 6 in January 2012. In 2010, the singer released two singles; "Nagging" alongside Lim Seul-ong and "Good Day", which both peaked atop the Gaon Digital Chart and became two of the best-selling singles in South Korea, accumulating more than 4 million total sales.


title: IU discography

text: Her second studio album "Last Fantasy" was released in November 2011 and was supported through the single "You & I". The album and the single debuted atop the South Korean charts with the album selling around 125,000 units and the single more than 6 million paid digital downloads, making it the second best-selling song in South Korea. IU's debut Japanese extended play "I□U" was released in December, debuting at no. 15 of the Oricon Albums Chart, selling about 12,000 copies. IU's fourth studio album "Palette" was released in April 2017 and supported through three singles; "Through the Night", "Can't Love You Anymore" and "Palette". The album debuted atop the Gaon Album Chart, selling a total of 97,000 copies. It became her first album to top the "Billboard" World Albums and peaked at no. 25 of the Top Heatseekers. Her ninth extended play "Love Poem" was released in November 2019. It debuted atop the Gaon Album Chart and became her best-selling album within two weeks, moving more than 160,000 physical copies. "Love Poem" was supported by two singles: "Love Poem" and "Blueming", both combined topping the charts for five weeks.


title: IU discography

text: Over the course of her career, IU has sold over one million albums and more than 120 million paid digital downloads (with the sales of collaborative singles, soundtracks, album tracks, and other appearances included), making her the best selling female and solo artist of South Korea. IU has scored the most number one songs in Korea with a record-breaking 30 number-one songs on the Gaon Digital Chart and 18 on the "Billboard" K-pop Hot 100.


title: Agranulocytosis

text: Agranulocytosis, also known as agranulosis or granulopenia, is an acute condition involving a severe and dangerous lowered white blood cell count (leukopenia, most commonly of neutrophils) and thus causing a neutropenia in the circulating blood. It is a severe lack of one major class of infection-fighting white blood cells. People with this condition are at very high risk of serious infections due to their suppressed immune system.


title: Agranulocytosis

text: In agranulocytosis, the concentration of granulocytes (a major class of white blood cells that includes neutrophils, basophils, and eosinophils) drops below 200 cells/mm of blood.


title: Agranulocytosis

text: Agranulocytosis may be asymptomatic, or may clinically present with sudden fever, rigors and sore throat. Infection of any organ may be rapidly progressive (e.g., pneumonia, urinary tract infection). Sepsis may also progress rapidly.


title: Agranulocytosis

text: A large number of drugs have been associated with agranulocytosis, including antiepileptics (such as carbamazepine and valproate), antithyroid drugs (carbimazole, thiamazole, and propylthiouracil), antibiotics (penicillin, chloramphenicol and trimethoprim/sulfamethoxazole), H2 blockers (cimetidine, famotidine, nizatidine, ranitidine), ACE inhibitors (benazepril), cytotoxic drugs, gold salts, analgesics (aminophenazone, indomethacin, naproxen, phenylbutazone, metamizole), mebendazole, allopurinol, the antidepressants mianserin and mirtazapine, and some antipsychotics. The atypical antipsychotic clozapine in particular is largely restricted to treatment-resistant cases and mandatory blood count monitoring in most countries.


title: Agranulocytosis

text: Although the reaction is generally idiosyncratic rather than proportional, experts recommend that patients using these drugs be told about the symptoms of agranulocytosis-related infection, such as a sore throat and a fever.


title: Agranulocytosis

text: The Centers for Disease Control and Prevention traced outbreaks of agranulocytosis among cocaine users, in the US and Canada between March 2008 and November 2009, to the presence of levamisole in the drug supply. The Drug Enforcement Administration reported that, as of February 2010, 71% of seized cocaine lots coming into the US contained levamisole as a cutting agent. Levamisole is an antihelminthic (i.e. deworming) drug used in animals. The reason for adding levamisole to cocaine is unknown, although it can be due to their similar melting points and solubilities.


title: Agranulocytosis

text: The diagnosis is made after a complete blood count, a routine blood test. The absolute neutrophil count in this test will be below 500, and can reach 0 cells/mm. Other kinds of blood cells are typically present in normal numbers. To formally diagnose agranulocytosis, other pathologies with a similar presentation must be excluded, such as aplastic anemia, paroxysmal nocturnal hemoglobinuria, myelodysplasia and leukemias. This requires a bone marrow examination that shows normocellular (normal amounts and types of cells) blood marrow with underdeveloped promyelocytes. These underdeveloped promyelocytes, if fully matured, would have been the missing granulocytes.


title: Agranulocytosis

text: The term "agranulocytosis" derives from the Greek: "a", meaning without; granulocyte, a particular kind of white blood cell (containing granules in its cytoplasm); and "osis", meaning condition [esp. disorder]. Consequently, agranulocytosis is sometimes described as "no granulocytes", but a total absence is not required for diagnosis.


title: Agranulocytosis

text: However, "-osis" is commonly used in blood disorders to imply cell proliferation (such as in "leukocytosis"), while "-penia" to imply reduced cell numbers (as in "leukopenia"); for these reasons, granulocytopenia is a more etymologically consistent term, and as such, is sometimes preferred to "agranulocytosis" (which can be misinterpreted as "agranulocyt-osis", meaning proliferation of agranulocytes (i.e. lymphocytes and monocytes). Despite this, "agranulocytosis" remains the most widely used term for the condition.


title: Agranulocytosis

text: The terms agranulocytosis, granulocytopenia and neutropenia are sometimes used interchangeably. Agranulocytosis implies a more severe deficiency than granulocytopenia. Neutropenia indicates a deficiency of neutrophils (the most common granulocyte cell) only.


title: Agranulocytosis

text: To be precise, neutropenia is the term normally used to describe absolute neutrophil counts (ANCs) of less than 500 cells per microlitre, whereas agranulocytosis is reserved for cases with ANCs of less than 100 cells per microlitre.


title: Agranulocytosis

text: In patients that have no symptoms of infection, management consists of close monitoring with serial blood counts, withdrawal of the offending agent (e.g., medication), and general advice on the significance of fever. Transfusion of granulocytes would be a solution to the problem. However, granulocytes live only ~10 hours in the circulation (for days in spleen or other tissue), which gives a very short-lasting effect. In addition, there are many complications of such a procedure.


title: Peroxide

text: In chemistry, peroxides are a group of compounds with the structure , where R = any element. The group in a peroxide is called the peroxide group or peroxo group. The nomenclature is somewhat variable.


title: Peroxide

text: The most common peroxide is hydrogen peroxide (), colloquially known simply as "peroxide". It is marketed as solutions in water at various concentrations. Many organic peroxides are known as well.


title: Lynn (voice actress)

text: Lynn was born in Yokosuka, Kanagawa, she is of mixed American and Japanese parentage. She became interested in acting while at nursery school. She had learned that her mother used to be part of bands, which influenced her interest in entertainment. Lynn watched "Case Closed" and "InuYasha", while in elementary school. While in middle school, she became aware of the . She later attended the school, after asking permission with her parents. She worked at the institute in her first year of high school; as she lived in Niigata Prefecture at that time, she would take the Shinkansen to Tokyo every Sunday for lessons. While attending high school, she became a manager of the school's basketball club. In her third year, she performed at the school's cultural festival; the positive reception she received for her performance inspired her to continue her pursuit. She continued her studies at the training school, while starting her voice acting roles. She initially voiced roles in Japanese dubs of foreign media, while voicing background characters in anime. After passing an audition, her first main role is Maya Kyōdō in the anime series "Sabagebu!". She played Lisesharte Atismata in "Undefeated Bahamut Chronicle", Mashiro Munetani in "High School Fleet" and Nozomi Kaminashi in "Keijo". She played Fuuka Akitsuki in "Fuuka" and performed insert songs for the series. Lynn played Himari Takanashi in "Interviews with Monster Girls", Mizuki Fudō in "Idol Incidents", Mano Rinoda in "Schoolgirl Strikers" and Ena Komiya in "Just Because!". She played Song Minhua in "Girly Air Force" and Mafuyu Kirisu in "We Never Learn". She enjoys horse racing and won the 99th Prix de l'Arc de Triomphe at Longchamp Racecourse in Paris, France on October 4, 2020 with a trifecta ticket of odds of 1010.8 times and the 65th Osaka Cup at Hanshin Racecourse on April 4, 2021 with a trifecta ticket of odds of 1062.1 times and popularity of 174. On April 4, 2021, she won the 65th Osaka Cup at Hanshin Racecourse by winning a trifecta ticket with odds of 1,062.1, the most popular horse in the race, for a payout of over one million yen.


title: Lynn (voice actress)

text: On July 29, 2022, during Lynn's appearance on the live-streaming program for "Engage Kiss", it was discovered that she was positive for COVID-19 after the PCR test she had taken a few days earlier revealed the result, forcing her to leave in the middle of the program.


title: Quotient group

text: A quotient group or factor group is a mathematical group obtained by aggregating similar elements of a larger group using an equivalence relation that preserves some of the group structure (the rest of the structure is "factored" out). For example, the cyclic group of addition modulo "n" can be obtained from the group of integers under addition by identifying elements that differ by a multiple of formula_1 and defining a group structure that operates on each such class (known as a congruence class) as a single entity. It is part of the mathematical field known as group theory.


title: Quotient group

text: For a congruence relation on a group, the equivalence class of the identity element is always a normal subgroup of the original group, and the other equivalence classes are precisely the cosets of that normal subgroup. The resulting quotient is written formula_2, where formula_3 is the original group and formula_4 is the normal subgroup. (This is pronounced formula_5, where formula_6 is short for modulo.)


title: Quotient group

text: Much of the importance of quotient groups is derived from their relation to homomorphisms. The first isomorphism theorem states that the image of any group "G" under a homomorphism is always isomorphic to a quotient of formula_3. Specifically, the image of formula_3 under a homomorphism formula_9 is isomorphic to formula_10 where formula_11 denotes the kernel of formula_12.


title: Quotient group

text: The dual notion of a quotient group is a subgroup, these being the two primary ways of forming a smaller group from a larger one. Any normal subgroup has a corresponding quotient group, formed from the larger group by eliminating the distinction between elements of the subgroup. In category theory, quotient groups are examples of quotient objects, which are dual to subobjects.


title: Quotient group

text: Given a group formula_3 and a subgroup formula_14, and an element formula_15, one can consider the corresponding left coset: formula_16. Cosets are a natural class of subsets of a group; for example consider the abelian group "G" of integers, with operation defined by the usual addition, and the subgroup formula_14 of even integers. Then there are exactly two cosets: formula_18, which are the even integers, and formula_19, which are the odd integers (here we are using additive notation for the binary operation instead of multiplicative notation).


title: Quotient group

text: For a general subgroup "formula_14", it is desirable to define a compatible group operation on the set of all possible cosets, formula_21. This is possible exactly when "formula_14" is a normal subgroup, see below. A subgroup formula_4 of a group "formula_3" is normal if and only if the coset equality formula_25 holds for all formula_15. A normal subgroup of "formula_3" is denoted formula_4.


title: Quotient group

text: Let "formula_4" be a normal subgroup of a group "formula_3" . Define the set formula_2 to be the set of all left cosets of "formula_4" in "formula_3" . That is, formula_34. Since the identity element formula_35, formula_36. Define a binary operation on the set of cosets, formula_2, as follows. For each formula_38 and formula_39 in formula_2, the product of formula_38 and formula_39, formula_43, is formula_44. This works only because formula_44 does not depend on the choice of the representatives, formula_46 and formula_47, of each left coset, formula_38 and formula_39. To prove this, suppose formula_50 and formula_51 for some formula_52. Then


title: Quotient group

text: This depends on the fact that "N" is a normal subgroup. It still remains to be shown that this condition is not only sufficient but necessary to define the operation on "G"/"N".


title: Quotient group

text: To show that it is necessary, consider that for a subgroup "formula_4" of "formula_3", we have been given that the operation is well defined. That is, for all formula_50 and formula_51"," for formula_58.


title: Quotient group

text: It can also be checked that this operation on formula_2 is always associative, formula_2 has identity element "formula_4", and the inverse of element formula_38 can always be represented by formula_71. Therefore, the set formula_2 together with the operation defined by formula_73 forms a group, the quotient group of "formula_3" by "formula_4".


title: Quotient group

text: Due to the normality of "formula_4", the left cosets and right cosets of "formula_4" in "formula_3" are the same, and so, formula_2 could have been defined to be the set of right cosets of "formula_4" in "formula_3" .


title: Quotient group

text: For example, consider the group with addition modulo 6: formula_82. Consider the subgroup "formula_83", which is normal because "formula_3" is abelian. Then the set of (left) cosets is of size three:


title: Quotient group

text: The binary operation defined above makes this set into a group, known as the quotient group, which in this case is isomorphic to the cyclic group of order 3.


title: Quotient group

text: The reason formula_2 is called a quotient group comes from division of integers. When dividing 12 by 3 one obtains the answer 4 because one can regroup 12 objects into 4 subcollections of 3 objects. The quotient group is the same idea, although we end up with a group for a final answer instead of a number because groups have more structure than an arbitrary collection of objects.


title: Quotient group

text: To elaborate, when looking at formula_2 with "formula_4" a normal subgroup of "formula_3", the group structure is used to form a natural "regrouping". These are the cosets of "formula_4" in "formula_3". Because we started with a group and normal subgroup, the final quotient contains more information than just the number of cosets (which is what regular division yields), but instead has a group structure itself.


title: Quotient group

text: Consider the group of integers formula_92 (under addition) and the subgroup formula_93 consisting of all even integers. This is a normal subgroup, because formula_92 is abelian. There are only two cosets: the set of even integers and the set of odd integers, and therefore the quotient group formula_95 is the cyclic group with two elements. This quotient group is isomorphic with the set formula_96 with addition modulo 2; informally, it is sometimes said that formula_95 "equals" the set formula_96 with addition modulo 2.


title: Quotient group

text: A slight generalization of the last example. Once again consider the group of integers formula_92 under addition. Let "n" be any positive integer. We will consider the subgroup formula_138 of formula_92 consisting of all multiples of "formula_1". Once again formula_138 is normal in formula_92 because formula_92 is abelian. The cosets are the collection formula_144. An integer "formula_145" belongs to the coset formula_146, where "formula_147" is the remainder when dividing "formula_145" by "formula_1". The quotient formula_150 can be thought of as the group of "remainders" modulo formula_1. This is a cyclic group of order "formula_1".


title: Quotient group

text: The twelfth roots of unity, which are points on the complex unit circle, form a multiplicative abelian group "formula_3", shown on the picture on the right as colored balls with the number at each point giving its complex argument. Consider its subgroup "formula_4" made of the fourth roots of unity, shown as red balls. This normal subgroup splits the group into three cosets, shown in red, green and blue. One can check that the cosets form a group of three elements (the product of a red element with a blue element is blue, the inverse of a blue element is green, etc.). Thus, the quotient group "formula_2" is the group of three colors, which turns out to be the cyclic group with three elements.


title: Quotient group

text: Consider the group of real numbers formula_156 under addition, and the subgroup formula_92 of integers. Each coset of formula_92 in formula_156 is a set of the form formula_160, where formula_46 is a real number. Since formula_162 and formula_163 are identical sets when the non-integer parts of "formula_164" and "formula_165" are equal, one may impose the restriction formula_166 without change of meaning. Adding such cosets is done by adding the corresponding real numbers, and subtracting 1 if the result is greater than or equal to 1. The quotient group formula_167 is isomorphic to the circle group, the group of complex numbers of absolute value 1 under multiplication, or correspondingly, the group of rotations in 2D about the origin, that is, the special orthogonal group formula_168. An isomorphism is given by formula_169 (see Euler's identity).


title: Quotient group

text: If "formula_3" is the group of invertible formula_171 real matrices, and "formula_4" is the subgroup of formula_171 real matrices with determinant 1, then "formula_4" is normal in "formula_3" (since it is the kernel of the determinant homomorphism). The cosets of "formula_4" are the sets of matrices with a given determinant, and hence "formula_2" is isomorphic to the multiplicative group of non-zero real numbers. The group "formula_4" is known as the special linear group formula_179.


title: Quotient group

text: Consider the abelian group formula_180 (that is, the set formula_181 with addition modulo 4), and its subgroup formula_182. The quotient group formula_183 is formula_184. This is a group with identity element formula_182, and group operations such as formula_186. Both the subgroup formula_182 and the quotient group formula_184 are isomorphic with formula_189.


title: Quotient group

text: Consider the multiplicative group formula_190. The set "formula_4" of formula_1th residues is a multiplicative subgroup isomorphic to formula_193. Then "formula_4" is normal in "formula_3" and the factor group "formula_2" has the cosets formula_197. The Paillier cryptosystem is based on the conjecture that it is difficult to determine the coset of a random element of "formula_3" without knowing the factorization of "formula_1".


title: Quotient group

text: The quotient group formula_200 is isomorphic to the trivial group (the group with one element), and formula_201 is isomorphic to "formula_3".


title: Quotient group

text: The order of "formula_2", by definition the number of elements, is equal to formula_204, the index of "formula_4" in "formula_3". If "formula_3" is finite, the index is also equal to the order of "formula_3" divided by the order of "formula_4". The set "formula_2" may be finite, although both "formula_3" and "formula_4" are infinite (for example, formula_95).


title: Quotient group

text: There is a "natural" surjective group homomorphism formula_214, sending each element formula_215 of "formula_3" to the coset of "formula_4" to which "formula_215" belongs, that is: formula_219. The mapping formula_220 is sometimes called the "canonical projection of formula_3 onto formula_2". Its kernel is "formula_4".


title: Quotient group

text: There is a bijective correspondence between the subgroups of "formula_3" that contain "formula_4" and the subgroups of "formula_2"; if formula_14 is a subgroup of "formula_3" containing "formula_4", then the corresponding subgroup of "formula_2" is formula_231. This correspondence holds for normal subgroups of "formula_3" and "formula_2" as well, and is formalized in the lattice theorem.


title: Quotient group

text: Several important properties of quotient groups are recorded in the fundamental theorem on homomorphisms and the isomorphism theorems.


title: Quotient group

text: If "formula_3" is abelian, nilpotent, solvable, cyclic or finitely generated, then so is "formula_2".