Talk:ZJ theorem

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 Field:  Algebra

Even p[edit]

The condition on this theorem is that p be an odd prime. Does anyone have a counterexample showing that it doesn't work when p=2? DavidLHarden (talk) 02:52, 6 January 2010 (UTC)

The wikipedia article follows Glauberman's article. The hypothesis is that G is p-stable. The definition given for p-stable is not useful when p=2 (a 2-stable group is 2-nilpotent, and so G/O2′(G)≅S is a 2-group and of course Z(J(S)) is normal in S). The standard replacement for 2-constrained+2-stable is 2-constrained+S4-free. Glauberman's original 1968 paper (referenced in our wiki article) gives example 10.2 on page 1132 to show that 2-constrained S4-free groups need not have ZJ(S) normal. JackSchmidt (talk) 05:54, 6 January 2010 (UTC)