\begin{definition}[Definition:Centralizer/Subgroup]
Let $\struct {G, \circ}$ be a group.
Let $H \le \struct {G, \circ}$.
The '''centralizer of $H$ (in $G$)''' is the set of elements of $G$ which commute with all $h \in H$:
:$\map {C_G} H = \set {g \in G: \forall h \in H: g \circ h = h \circ g}$
\end{definition}