Abelian quotient
= Abelian quotient
An abelian quotient is a <quotient group> $G/N$ that is an <abelian group>. It exists only for a <normal subgroup> $N$, and it is abelian exactly when $N$ contains the <commutator subgroup>. Thus every abelian quotient factors through the <abelianization> $G/[G,G]$.