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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

  1. $\mathcal{Z}_5$
  2. $\mathcal{Z}_{10}$
  3. $\mathcal{Z}_2$
  4. $\mathcal{Z}_{30}$
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@Amit. Zn is isomorphic to G. So, Zn must also be a group, right? Now, I have a query.

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

Dont know if my thinking is right.

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