Let $G$ be a semigroup and let $S$ be a subset of $G$. The centralizer of $S$ is \(C_G(S) = \{g\in G\mid gs=sg \text{ for all } s\in S\}.\) When $G$ is a group, we can also say \(C_G(S) = \{g\in G\mid gsg^{-1} =s \text{ for all } s\in S\}.\)
Wikidata ID: Q190629