Definition:Abelianization of Group

Definition
Let $G$ be a group.

Its abelianization is the quotient by its commutator subgroup:
 * $G^{\operatorname{ab}} = G / \left[{G, G}\right]$

Also see

 * Abelianization of Group is Largest Abelian Quotient
 * Universal Property of Abelianization of Group
 * Definition:Abelianization of Group Functor