Abelian Group

up:: Group

A group $(G,\cdot )$ is said to be Abelian when its operation is commutative. That is,

$$\forall a,b\in G,ab=ba$$

Properties

Abelianization

To any group $G$ one can perform what is called an Abelianization: quotienting by the subgroup of the commutators "$ab-ba$" $=ab(ba{)}^{-1}$.