Assume the following are isomorphic:
Prove |G| = |H|
Prove "phi"(eG) = eH.
Prove "phi"(a^n) = ("phi"(a))^n.
Let $\displaystyle \phi$ be an isomophism between G and H.
$\displaystyle \phi$ is a bijection, what does that tell you about |G| and |H|?
$\displaystyle \phi(e_G) = \phi(e_G^2) = \phi(e_G)\phi(e_G) = \phi(e_G)^2$
What does this tell you about $\displaystyle \phi(e_G)$?
Can you induct on a similar expression that I've used above?