# Definition:Abelianization of Group

## Definition

Let $G$ be a group.

Its abelianization is the quotient by its commutator subgroup:

$G^{\mathrm {ab} } = G / \sqbrk {G, G}$

## Linguistic Note

The British English form of abelianization is abelianisation.

On $\mathsf{Pr} \infty \mathsf{fWiki}$ it is the norm to use American English, so the spelling abelianisation will rarely be encountered here, if at all.