Hi All:

I study a little abstravt algebra when I have time, which isn't very often. Here is one I was looking over and trying to show.

I know that a homomorphism preserves operations. Example

$\displaystyle e^{x}$ is homorphic because $\displaystyle e^{a}\cdot e^{b}=e^{a+b}$. It has all the criteria of a homomorphism. It maps multiplication to addition.

But, in general how can we show that if G is an abelian group (That is, ab=ba), Let $\displaystyle f: \;\ G\rightarrow H$ be a surjective homomorphism of groups. Prove H is abelian.