Let \(G\) be a group and \(S\subseteq G\) a subset. The centralizer of \(S\) in \(G\) is \[ Z_G(S) \coloneqq \theset{g\in G \st gsg^{-1} = s \text{ for every } s\in S}. \]
What is the centralizer $Z_G(S)$?
Centralizer $Z_G(S)$ of a subset
FD-SSR6N
FD-SSR6N
Let \(G\) be a group and \(S\subseteq G\) a subset. The centralizer of \(S\) in \(G\) is \[ Z_G(S) \coloneqq \theset{g\in G \st gsg^{-1} = s \text{ for every } s\in S}. \]