# Abelian group

An **abelian group**, also called a * commutative group*, is a group (G, * ) such that g

_{1}* g

_{2}= g

_{2}* g

_{1}for all g

_{1}and g

_{2}in G, where * is a binary operation in G. This means that the order in which the

Groups that are not commutative are called non-abelian (rather than non-commutative).

Abelian groups are named after