### Abstract

The Schur multiplier of a fusion system F on a finite p-group P, being defined as the inverse limit of the Schur multipliers of the subgroups of P taken over the category F, has a series of properties analogous to some properties of Schur multipliers of finite groups. This is one of the tools used in [R. Kessar, The Solomon system F-Sol(3) does not occur as fusion system of a 2-block, preprint, 2004] to show that the Solomon fusion system cannot arise as the Brauer category of a p-block of a finite group. (c) 2005 Elsevier Inc. All rights reserved.

Original language | English |
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Pages (from-to) | 402-408 |

Number of pages | 6 |

Journal | Journal of Algebra |

Volume | 296 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2006 |

### Cite this

*Journal of Algebra*,

*296*(2), 402-408. https://doi.org/10.1016/j.jalgebra.2005.03.039

**A note on the Schur multiplier of a fusion system.** / Linckelmann, Markus.

Research output: Contribution to journal › Article

*Journal of Algebra*, vol. 296, no. 2, pp. 402-408. https://doi.org/10.1016/j.jalgebra.2005.03.039

}

TY - JOUR

T1 - A note on the Schur multiplier of a fusion system

AU - Linckelmann, Markus

PY - 2006

Y1 - 2006

N2 - The Schur multiplier of a fusion system F on a finite p-group P, being defined as the inverse limit of the Schur multipliers of the subgroups of P taken over the category F, has a series of properties analogous to some properties of Schur multipliers of finite groups. This is one of the tools used in [R. Kessar, The Solomon system F-Sol(3) does not occur as fusion system of a 2-block, preprint, 2004] to show that the Solomon fusion system cannot arise as the Brauer category of a p-block of a finite group. (c) 2005 Elsevier Inc. All rights reserved.

AB - The Schur multiplier of a fusion system F on a finite p-group P, being defined as the inverse limit of the Schur multipliers of the subgroups of P taken over the category F, has a series of properties analogous to some properties of Schur multipliers of finite groups. This is one of the tools used in [R. Kessar, The Solomon system F-Sol(3) does not occur as fusion system of a 2-block, preprint, 2004] to show that the Solomon fusion system cannot arise as the Brauer category of a p-block of a finite group. (c) 2005 Elsevier Inc. All rights reserved.

U2 - 10.1016/j.jalgebra.2005.03.039

DO - 10.1016/j.jalgebra.2005.03.039

M3 - Article

VL - 296

SP - 402

EP - 408

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

IS - 2

ER -