The **abelianization** of a group $G$ is $G/[G,G]$, the quotient by its commutator subgroup. The abelianization of $G$ is the largest abelian quotient of $G$ in the sense that any homomorphism $G\to A$ where $A$ is an abelian group factors as a composition of homomorphisms $G\to G/G'\to A$.

**Authors:**

**Knowl status:**

- Review status: beta
- Last edited by Sam Schiavone on 2021-07-12 19:22:19

**Referred to by:**

**History:**(expand/hide all)

**Differences**(show/hide)