nLab
centralizer

Contents

Definition

The centralizer of a subset SS of a group GG is the set C G(S)C_G(S) of all elements cGc\in G such that cs=scc s=s c for all sSs\in S. It is the largest subgroup HH of GG containing SS such that SS is in the center of HH. The centralizer of a subset is clearly a subgroup of its normalizer, as fixing the set gH=Hgg H=H g is a weaker requirement than gh=hgg h=h g for all hHh\in H.

Revised on November 1, 2013 06:40:02 by Urs Schreiber (145.116.130.141)