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About: Z* theorem     Goto   Sponge   NotDistinct   Permalink

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Type: yago:WikicatTheoremsInGroupTheoryyago:Abstraction100002137yago:Communication100033020yago:Group100031264yago:Message106598915yago:Proposition106750804yago:Statement106722453yago:Theorem106752293yago:WikicatFiniteGroups New Facet based on Instances of this Class

In mathematics, George Glauberman's Z* theorem is stated as follows: Z* theorem: Let G be a finite group, with O(G) being its maximal normal subgroup of odd order. If T is a Sylow 2-subgroup of G containing an involution not conjugate in G to any other element of T, then the involution lies in Z*(G), which is the inverse image in G of the center of G/O(G). This generalizes the Brauer–Suzuki theorem (and the proof uses the Brauer–Suzuki theorem to deal with some small cases).