Definition:Abelian Group

An Abelian group is a group $$G$$ where $$\forall a,b \in G,$$ $$ab=ba$$. That is, every element in $$G$$ commutes with every other element in $$G$$.

Equivalently, $$G$$ is Abelian if and only if $$G=Z(G)$$, where $$Z(G)$$ denotes the center of $$G$$.