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Endotrivial modules for the general linear group in a nondefining characteristic

Carlson, Jon and Mazza, Nadia and Nakano, Daniel (2014) Endotrivial modules for the general linear group in a nondefining characteristic. Mathematische Zeitschrift, 278 (3-4). pp. 901-925. ISSN 0025-5874

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    Abstract

    Suppose that $G$ is a finite group such that $\SL(n,q)\subseteq G \subseteq \GL(n,q)$, and that $Z$ is a central subgroup of $G$. Let $T(G/Z)$ be the abelian group of equivalence classes of endotrivial $k(G/Z)$-modules, where $k$ is an algebraically closed field of characteristic~$p$ not dividing $q$. We show that the torsion free rank of $T(G/Z)$ is at most one, and we determine $T(G/Z)$ in the case that the Sylow $p$-subgroup of $G$ is abelian and nontrivial. The proofs for the torsion subgroup of $T(G/Z)$ use the theory of Young modules for $\GL(n,q)$ and a new method due to Balmer for computing the kernel of restrictions in the group of endotrivial modules.

    Item Type: Article
    Journal or Publication Title: Mathematische Zeitschrift
    Additional Information: The original publication is available at www.link.springer.com
    Subjects:
    Departments: Faculty of Science and Technology > Mathematics and Statistics
    ID Code: 69712
    Deposited By: ep_importer_pure
    Deposited On: 18 Jun 2014 08:48
    Refereed?: Yes
    Published?: Published
    Last Modified: 16 Dec 2017 05:03
    Identification Number:
    URI: http://eprints.lancs.ac.uk/id/eprint/69712

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