# Math Help - abstract

1. ## abstract

Assume the following are isomorphic:

Prove |G| = |H|

Prove "phi"(eG) = eH.

Prove "phi"(a^n) = ("phi"(a))^n.

2. Let $\phi$ be an isomophism between G and H.

$\phi$ is a bijection, what does that tell you about |G| and |H|?

$\phi(e_G) = \phi(e_G^2) = \phi(e_G)\phi(e_G) = \phi(e_G)^2$

What does this tell you about $\phi(e_G)$?

Can you induct on a similar expression that I've used above?