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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^{-1^st} =s² > an HNN extention of H which embedds H in the obvious way.

Let S = {s}. Then t^{-1^st} 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)[reply]

Typos

I don't want to make the edit myself, in case I am mistaken, but in the first sentance:

In group theory, the centralizer and normalizer of a subset S of a group G are subgroups of G which have a restricted action on the elements of S and S as a whole, respectively. These subgroups provide insight into the structure of G.

Shouldn't it infact read:

In group theory, the centralizer and normalizer of a subset S of a group G are subgroups of G which have a restricted action on the elements of S and G as a whole, respectively. These subgroups provide insight into the structure of G.

James.robinson (talk) 07:46, 1 January 2009 (UTC)[reply]