surjective homomorphism

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

$e^{x}$ is homorphic because $e^{a}\cdot e^{b}=e^{a+b}$ . 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 $f: \;\ G\rightarrow H$ be a surjective homomorphism of groups. Prove H is abelian.