Assume the following are isomorphic:

Prove |G| = |H|

Prove "phi"(eG) = eH.

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

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- Mar 16th 2009, 11:50 AMpila0688abstract
Assume the following are isomorphic:

Prove |G| = |H|

Prove "phi"(eG) = eH.

Prove "phi"(a^n) = ("phi"(a))^n. - Mar 16th 2009, 01:56 PMSimonM
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?