Group theory

Question

Let $G$ be a group whose presentation is

$G=\{ x, y \mid x^5 =y^2 =e, \:\:\:\: x^2y=yx\}$,

$\mathcal{Z}_n$: Set of integers modulo $n$

Then $G$ is isomorphic to

• A. $\mathcal{Z}_5$
• B. $\mathcal{Z}_{10}$
• C. $\mathcal{Z}_2$
• D. $\mathcal{Z}_{30}$

Answer 1

@Amit. Z_n is isomorphic to G. So, Z_n must also be a group, right? Now, I have a query.

Can Z_n = set of integers modulo n  can ever be a group  because inverse of 0 never exists.

Dont know if my thinking is right.

Comments

is (C) the answer?