abelian group

An abelian group or commutative group is a group in which the group operation is commutative.

Formally,
An abelian group is the algebraic structure consisting of a set $A$ together with a binary operation such that for any two elements $x,y$ of $A$, we have $$xy=yx$$in addition to the other properties of a group.

A group is abelian if and only if its Cayley table is symmetric about the main diagonal.

Examples

The group center $Z(G)$ of any group $G$