Definition:Centralizer/Group Subset

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

Let $S \subseteq G$.

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


 * $C_G \left({S}\right) = \left\{{x \in G: \forall s \in S: x \circ s = s \circ x}\right\}$

Also denoted as
The notation $C \left({S; G}\right)$ is sometimes seen for the centralizer of $S$ in $G$.

Linguistic Note
The UK English spelling of this is centraliser.