Center (group theory)

The center of a group $G$ (denoted $Z(G)$) is the set of all elements which commute with every element of the group. That is, the center of $G$ is $\{a\in G:ab=ba\ \forall b\in G\}$.

Facts

• If $G$ is a group, the center $Z(G)$ is a normal subgroup of $G$.
• We have $Z(G)=G$ if and only if $G$ is an abelian group.

External links

• Center on MathWorld