\begin{definition}[Definition:Centralizer/Group Element]
Let $\struct {G, \circ}$ be a group.
Let $a \in \struct {G, \circ}$.
The '''centralizer of $a$ (in $G$)''' is defined as:
:$\map {C_G} a = \set {x \in G: x \circ a = a \circ x}$
That is, the centralizer of $a$ is the set of elements of $G$ which commute with $a$.
\end{definition}