Endotrivial modules for the sporadic simple groups and their covers

TL;DR

This paper explores endotrivial modules in sporadic simple groups and their covers, revealing the existence of non-trivial torsion modules with larger dimensions for groups with higher p-rank.

Contribution

It provides the first detailed analysis of endotrivial modules for sporadic groups, identifying new torsion modules with significant dimensions.

Findings

Existence of torsion endotrivial modules with dimension > 1

Identification of such modules in several sporadic groups

Focus on groups with p-rank greater than one

Abstract

In a step towards the classification of endotrivial modules for quasi-simple groups, we investigate endotrivial modules for the sporadic simple groups and their covers. A main outcome of our study is the existence of torsion endotrivial modules with dimension greater than one for several sporadic groups with $p$-rank greater than one.