High Quality Content by WIKIPEDIA articles! In mathematics, George Glauberman's ZJ theorem states that if a finite group G is p-constrained and p-stable and has a normal p-subgroup for some odd prime p, then Op?(G)Z(J(S)) is a normal subgroup of G, for any Sylow p-subgroup S. J(S) is the Thompson subgroup of a p-group S: the subgroup generated by the abelian subgroups of maximal order; Z(H) means the center of a group H.; Op? is the maximal normal subgroup of G of order coprime to p, the p?-core; Op is the maximal normal p-subgroup of G, the p-core; Op?,p(G) is the maximal normal p-nilpotent subgroup of G, the p?,p-core, part of the upper p-series.

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