Talk:Centralizer and normalizer

The statement:

• The normalizer gets its name from the fact that if we let <S> be the subgroup generated by S, then N(S) is the largest subgroup of G having <S> as a normal subgroup.

is incorrect.

Let H = < s | s³ = 1 > the cyclic group of order 3.

Let G = <s, t | s³ = 1 , t^{-1st =s2 > an HNN extention of H which embedds H in the obvious way.}

Let S = {s}. Then t^{-1st is not in S so t is not in N_S(G). However it is contained in N_H(G), which (since H=<S>) is the largest subgroup of G having <S> as a normal subgroup. Bernard Hurley 21:50, 6 October 2006 (UTC)}