Definition:Abelianization of Group
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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
- Results about abelianizations of groups can be found here.
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.
Sources
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): Abelianization
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): commutator