Definition:Abelianization of Group

Definition
Let $G$ be a group.

The abelianization of $G$ is the quotient of $G$ by its derived subgroup:
 * $G^{\mathrm {ab} } = G / \sqbrk {G, G}$

Also see

 * Derived Subgroup is Normal, ensuring the validity of this definition


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