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

[img]
Preview
PDF (gl-rev6)
gl_rev6.pdf - Accepted Version

Download (419kB)

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:
Journal Article
Journal or Publication Title:
Mathematische Zeitschrift
Additional Information:
The original publication is available at www.link.springer.com
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600
Subjects:
ID Code:
69712
Deposited By:
Deposited On:
18 Jun 2014 07:48
Refereed?:
Yes
Published?:
Published
Last Modified:
07 Jul 2020 03:23