Definition:Centralizer/Subgroup

Definition

Let $\left({G, \circ}\right)$ be a group.

Let $H \le \left({G, \circ}\right)$.

The centralizer of $H$ (in $G$) is the set of elements of $G$ which commute with all $h \in H$:

$C_G \left({H}\right) = \left\{{g \in G: \forall h \in H: g \circ h = h \circ g}\right\}$

Notes

The UK English spelling of this is centraliser.

Sources

• John F. Humphreys: A Course in Group Theory (1996): $\S 10$: Definition $10.24$