Center

Let \(G\) be a group. The center of \(G\) is the subgroup \[ Z(G) \coloneqq \theset{ g\in G \st gh = hg \text{ for all } h\in G} = \theset{ g\in G \st C_G(g) = G }, \] where \(C_G(g)\) is the centralizer of \(g\). Its elements are the central elements of \(G\).