The torsion group of endotrivial modules

Carlson, Jon; Thévenaz, Jacques

doi:10.2140/ant.2015.9.749

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The torsion group of endotrivial modules

Jon F. Carlson and Jacques Thévenaz

Vol. 9 (2015), No. 3, 749–765

DOI: 10.2140/ant.2015.9.749

Abstract

Let $G$ be a finite group and let $T (G)$ be the abelian group of equivalence classes of endotrivial $k G$ -modules, where $k$ is an algebraically closed field of characteristic $p$ . We determine, in terms of the structure of $G$ , the kernel of the restriction map from $T (G)$ to $T (S)$ , where $S$ is a Sylow $p$ -subgroup of $G$ , in the case when $S$ is abelian. This provides a classification of all torsion endotrivial $k G$ -modules in that case.

Keywords

modular representation theory

Mathematical Subject Classification 2010

Primary: 20C20

Milestones

Received: 5 November 2014

Revised: 28 January 2015

Accepted: 27 February 2015

Published: 17 April 2015

Authors

Jon F. Carlson
Department of Mathematics University of Georgia Athens, GA 30602 United States

Jacques Thévenaz
Section de mathématiques EPFL Station 8 CH-1015 Lausanne Switzerland

Vol. 9, No. 3, 2015