Talk:Abelian Group Factored by Prime

I believe this proof is incomplete. In particular, the fact that $|H|=p^n$ is not proven. One way is via Cauchey's theorem: Suppose a prime other than $p$ divided $|H|$, say $q$. Then by Cauchey's theorem there exists an element $h\in H$ of order $q$. Since $h^{p^n}=e$, it must be that $q|p^n$, which is impossible. Now suppose $p$ divides $|K|$, then $K$ has an element of order $p$, which again will lead to a contradiction.


 * You're probably right. Feel free to create a user account and amend as appropriate. --prime mover 09:03, 2 May 2011 (CDT)