The torsion group of endotrivial modules

Abstract

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.

References in corpus (1)

• Endotrivial modules for the sporadic simple groups and their covers

Cited by in corpus (3)

• Endotrivial modules for finite groups via homotopy theory
• Torsion Free Endotrivial Modules for Finite Groups of Lie Type
• Endotrivial representations of finite groups and equivariant line bundles on the Brown complex