Caroline Lassueur

Simple endotrivial modules for linear, unitary and exceptional groups

Motivated by a recent result of Robinson showing that simple endotrivial modules essentially come from quasi-simple groups we classify such modules for finite special linear and unitary groups as well as for exceptional groups of Lie type. Our main tool is a lifting result for endotrivial modules obtained in a previous paper which allows us to apply character theoretic methods. As one application we prove that the

Endo-trivial modules for finite groups with dihedral Sylow 2-subgroup

\ell

Simple endotrivial modules for quasi-simple groups

ℓ-rank of quasi-simple groups possessing a faithful simple endotrivial module is at most 2. As a second application we complete the proof that principal blocks of finite simple groups cannot have Loewy length 4, thus answering a question of Koshitani, Külshammer and Sambale. Our results also imply a vanishing result for irreducible characters of special linear and unitary groups.

Relative projectivity and relative endotrivial modules

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 1 for several sporadic groups with p-rank greater than 1.

The Dade group of a finite group

Abstract We provide a description of the torsion subgroup 𝑇𝑇 ⁢ ( G )

Endotrivial Modules for the Schur Covers of the Symmetric and Alternating Groups

{\mathit{TT}(G)}

Lifting endo-p-permutation modules

of the finitely generated abelian group T ⁢ ( G )

Endo-trivial modules: a reduction to p"-central extensions

{T(G)}