So this is what I have:Let A be an abelian group and let B be a subgroup of A. Prove that A/B is abelian.

Let , then . We must show

Since B is a subgroup of A and A is abelian, then B is a normal subgroup of B.

We compute:

because B is a normal subgroup of A.

because A is abelian

And so A/B is abelian. Is this right?