This set inherits a group operation (sometimes called coset multiplication, or coset addition) from the original group G: (gN) • (hN) = (gh)N for all g and h in G. This definition is motivated by the idea (itself an instance of general structural considerations outlined above) that the map G → G / N that associates to any element g its coset gN be a group homomorphism, or by general abstract considerations called universal properties. The coset eN = N serves as the identity in this group, and the inverse of gN in the quotient group is (gN)−1 = (g−1)N.e[›] COUNT 3
QSN1 What is another term for coset multiplication? ANS1 coset addition QSN2 What group operation is taken by the set from the original group? ANS2 coset multiplication QSN3 What group does the inverse of gN include? ANS3 quotient group