## Abstract

For

Glauberman functor

*p*an odd prime, we generalise the Glauberman-Thompson*p*nilpotency theorem (Gorenstein, 1980) to arbitrary fusion systems. We define a notionofQd(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 anyGlauberman functor

*W*, generalising Glauberman’s*ZJ*-theorem (Glauberman, 1968) to arbitrary fusion systems.Original language | English |
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Pages (from-to) | 3093-3106 |

Number of pages | 14 |

Journal | Transactions of the American Mathematical Society |

Volume | 360 |

Issue number | 6 |

Early online date | 25 Jan 2008 |

DOIs | |

Publication status | Published - Jun 2008 |

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