\begin{definition}[Definition:Center (Abstract Algebra)/Group]
The '''center of a group''' $G$, denoted $\map Z G$, is the subset of elements in $G$ that commute with every element in $G$.
Symbolically:
:$\map Z G = \map {C_G} G = \set {g \in G: g x = x g, \forall x \in G}$
That is, the '''center''' of $G$ is the centralizer of $G$ in $G$ itself.
\end{definition}