Can you show example a group of order $p^2$ besides $Z_{p^2} $ and $Z_p \oplus Z_p$?

Asked Mar 28 '16 at 12:37

Active Mar 28 '16 at 12:39

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I want to find example a group of order $p^2$ (p is prime) besides $Z_{p^2} $ (group of integer under addition modulo $p^2$) , and $Z_p \oplus Z_p$ (external direct product of groups of integer under addition modulo p)

edited Mar 28 '16 at 12:39

asked Mar 28 '16 at 12:37

Agus Ahmad Rizqi

2

Note: the critical observation is that all such groups are abelian. you can find proofs of that, e.g., here – lulu Mar 28 '16 at 12:41
Thanks for the idea. It is useful for me – Agus Ahmad Rizqi Mar 30 '16 at 09:38

Can you show example a group of order $p^2$ besides $Z_{p^2} $ and $Z_p \oplus Z_p$?

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