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
is homorphic because . 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 be a surjective homomorphism of groups. Prove H is abelian.