If G is an abelian group and N is a subgroup of G, show that G/N is an abelian group observing that G/N is a homomorphic image of G.
Please show steps, I'm super confused.
Thanks!
First of all every subgroup of an abelian group is normal. This is obvious because , so .
by this is a homomorphism from onto G/N with kernel N. The point is it is a homomorphism from an abelian group, so the image group is abelian. G/N is a group because N is normal.
By this observation, G/N is abelian