Find all subgroups of $\Bbb Z_5 \times \Bbb Z_5$. I can see that the non-trivial ones are of order $5$. But how do I find them exactly?
Thanks for any help.
Find all subgroups of $\Bbb Z_5 \times \Bbb Z_5$. I can see that the non-trivial ones are of order $5$. But how do I find them exactly?
Thanks for any help.
We list the subgroups of order $5$. There is the group generated by $(0,1)$. Then there are the groups generated by $(1,b)$, where $b$ is an element of $\mathbb{Z}_5$. That's all. We can if we wish give the addition table for each.