### Abstract

For p an odd prime, we generalise the Glauberman-Thompson pnilpotency theorem (Gorenstein, 1980) to arbitrary fusion systems. We de. ne 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 (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 |

DOIs | |

Publication status | Published - 25 Jan 2008 |

### Keywords

- FINITE-GROUPS
- SUBGROUP
- BLOCKS

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## Cite this

Kessar, R., & Linckelmann, M. (2008). ZJ-theorems for fusion systems.

*Transactions of the American Mathematical Society*,*360*(6), 3093-3106. https://doi.org/10.1090/S0002-9947-08-04275-X