500 research outputs found

    ZJ-theorems for fusion systems

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    For p an odd prime, we generalise the Glauberman-Thompson p-nilpotency theorem [5, Ch. 8, Theorem 3.1] to arbitrary fusion systems. We define a notion of Qd(p)- free fusion systems and show that if F is a Qd(p)-free fusion system on some finite p-group P then F is controlled by W(P) for any Glauberman functor W, generalising Glauberman’s ZJ-theorem [3] to arbitrary fusion systems

    A block theoretic analogue of a theorem of Glauberman and Thompson

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    If p is an odd prime, G a finite group and P a Sylow-p-subgroup of G, a theorem of Glauberman and Thompson states that G is p-nilpotent if and only if NG(Z(J(P))) is p-nilpotent, where J(P) is the Thompson subgroup of P generated by all abelian subgroups of P of maximal order. Following a suggestion of G. R. Robinson, we prove a block-theoretic analogue of this theorem
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