On simple endotrivial modules

TL;DR

This paper investigates simple endotrivial modules over finite groups, demonstrating that their study can be simplified to quasi-simple groups when the group contains a specific elementary Abelian subgroup.

Contribution

It reduces the classification of non-monomial simple endotrivial modules to the case of quasi-simple groups under certain subgroup conditions.

Findings

Reduction to quasi-simple groups for classification

Focus on groups with elementary Abelian subgroups of order p^2

Simplification of the study of non-monomial modules

Abstract

We show that when G is a finite group which contains an elementary Abelian subgroup of order p^2 and k is an algebraically closed field of characteristic p, then the study of simple endotrivial kG-modules which are not monomial may be reduced to the case when G is quasi-simple.