1.6.71 Fields, Groups, Rings

Condition: Let \( G \) be abelian, and \( H \) be some of its subgroups. Prove that \( G / H \) is Abelian. Give an example of a non-commutative group \(A\) and its nontrivial normal subgroup \(B\) such that \(A / B\) is Abelian.