Diaz, Antonio and Glesser, Adam and Mazza, Nadia and Park, Sejong (2009) *Glauberman and Thompson's theorems for fusion systems.* Proceedings of the American Mathematical Society, 137. pp. 495-509.

| PDF (dgmpV2.0.pdf) Download (170Kb) | Preview |

Official URL: http://dx.doi.org/10.1090/S0002-9939-08-09690-1

## Abstract

We prove analogues of results of Glauberman and Thompson for fusion systems. Namely, given a (saturated) fusion system $\CF$ on a finite $p$-group $S$, and in the cases where $p$ is odd or $\CF$ is $S_4$-free, we show that $\Z(\N_\CF(\J(S)))=\Z(\CF)$ (Glauberman), and that if $\C_\CF(\Z(S))=\N_\CF(\J(S))=\CF_S(S)$, then $\CF=\CF_S(S)$ (Thompson). As a corollary, we obtain a stronger form of Frobenius' theorem for fusion systems, applicable under the above assumptions, and generalizing another result of Thompson.

Item Type: | Article |
---|---|

Journal or Publication Title: | Proceedings of the American Mathematical Society |

Additional Information: | First published in Proceedings of the American Mathematical Society in 137, 2009, published by the American Mathematical Society. Copyright 2008, American Mathematical Society |

Subjects: | Q Science > QA Mathematics |

Departments: | Faculty of Science and Technology > Mathematics and Statistics |

ID Code: | 20813 |

Deposited By: | Dr Nadia Mazza |

Deposited On: | 03 Dec 2008 11:07 |

Refereed?: | No |

Published?: | Published |

Last Modified: | 09 Oct 2013 12:43 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/20813 |

### Actions (login required)

View Item |