Which of the following groups is not cyclic? 
Which of the following groups is not cyclic?
(a) $G_1 = \{2, 4,6,8 \}$ w.r.t. $\odot$
(b) $G_2 = \{0,1, 2,3 \}$ w.r.t. $\oplus$ (binary XOR)
(c) $G_3 =$ Group of symmetries of a rectangle w.r.t. $\circ$ (composition)
(d) $G_4 =$ $4$th roots of unity w.r.t. $\cdot$ (multiplication)

Can anyone explain me this question?

Hint:  For a group to be cyclic, there must be an element $a$ so that all the elements can be expressed as $a^n$, each for a different $n$.  The terminology comes because this is the structure of $\Bbb {Z/Z_n}$, where $a=1$ works (and often others).  I can't see what the operator is in your first example-it is some sort of unicode.  For b, try each element $\oplus$ itself.  What do you get?  For c, there are two different types of symmetry-those that turn the rectangle upside down and those that do not.
