### Abstract

Original language | English |
---|---|

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 |

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### Keywords

- FINITE-GROUPS
- SUBGROUP
- BLOCKS

### Cite this

*Transactions of the American Mathematical Society*,

*360*(6), 3093-3106. https://doi.org/10.1090/S0002-9947-08-04275-X

**ZJ-theorems for fusion systems.** / Kessar, Radha; Linckelmann, Markus.

Research output: Contribution to journal › Article

*Transactions of the American Mathematical Society*, vol. 360, no. 6, pp. 3093-3106. https://doi.org/10.1090/S0002-9947-08-04275-X

}

TY - JOUR

T1 - ZJ-theorems for fusion systems

AU - Kessar, Radha

AU - Linckelmann, Markus

PY - 2008/1/25

Y1 - 2008/1/25

N2 - 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.

AB - 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.

KW - FINITE-GROUPS

KW - SUBGROUP

KW - BLOCKS

U2 - 10.1090/S0002-9947-08-04275-X

DO - 10.1090/S0002-9947-08-04275-X

M3 - Article

VL - 360

SP - 3093

EP - 3106

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 6

ER -