Lancaster EPrints

Glauberman and Thompson's theorems for fusion systems.

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.

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

    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