Yes, that is correct.
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.
because B is a normal subgroup of A.
because A is abelian
And so A/B is abelian. Is this right?