Endotrivial modules for the Schur covers of the symmetric and alternating groups

TL;DR

This paper classifies and describes the structure of endotrivial modules for Schur covers of symmetric and alternating groups across all characteristics, providing explicit generators and relations.

Contribution

It offers a complete description of the group of endotrivial modules for these covers, including generators and relations, in all cases.

Findings

Explicit group structure of endotrivial modules determined

Generators and relations provided for all characteristics

Complete classification achieved

Abstract

We investigate the endotrivial modules for the Schur covers of the symmetric and alternating groups and determine the structure of their group of endotrivial modules in all characteristics. We provide a full description of this group by generators and relations in all cases.