# Definition:Centralizer/Subgroup

## Definition

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 $h \in H$:

$\map {C_G} H = \set {g \in G: \forall h \in H: g \circ h = h \circ g}$

## Also see

• Results about centralizers can be found here.

## Linguistic Note

The UK English spelling of centralizer is centraliser.