Hi everyone!

I have the next problem:

$\displaystyle G$ a finit group which has order $\displaystyle n$ and $\displaystyle \varphi:G\rightarrow G$ defined by $\displaystyle \varphi(a)=a^m\;\forall\;a\in G$, I need to find a necessary and sufficient condition so that $\displaystyle \varphi$ is an isomorphism.

Any suggestion?

Thanks in advance!