Vol. 9, No. 3, 2015

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The torsion group of endotrivial modules

Jon F. Carlson and Jacques Thévenaz

Vol. 9 (2015), No. 3, 749–765

Let G be a finite group and let T(G) be the abelian group of equivalence classes of endotrivial kG-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 kG-modules in that case.

modular representation theory
Mathematical Subject Classification 2010
Primary: 20C20
Received: 5 November 2014
Revised: 28 January 2015
Accepted: 27 February 2015
Published: 17 April 2015
Jon F. Carlson
Department of Mathematics
University of Georgia
Athens, GA 30602
United States
Jacques Thévenaz
Section de mathématiques
Station 8
CH-1015 Lausanne