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Thick subcategories of the stable module category

D. Benson;  Jon Carlson;  Jeremy Rickard — 1997

Fundamenta Mathematicae

We study the thick subcategories of the stable category of finitely generated modules for the principal block of the group algebra of a finite group G over a field of characteristic p. In case G is a p-group we obtain a complete classification of the thick subcategories. The same classification works whenever the nucleus of the cohomology variety is zero. In case the nucleus is nonzero, we describe some examples which lead us to believe that there are always infinitely many thick subcategories concentrated...

Endotrivial modules over groups with quaternion or semi-dihedral Sylow 2-subgroup

Jon F. Carlson;  Nadia Mazza;  Jacques Thévenaz — 2013

Journal of the European Mathematical Society

Let G be a finite group with a Sylow 2-subgroup P which is either quaternion or semi-dihedral. Let k be an algebraically closed field of characteristic 2. We prove the existence of exotic endotrivial k G -modules, whose restrictions to P are isomorphic to the direct sum of the known exotic endotrivial k P -modules and some projective modules. This provides a description of the group T ( G ) of endotrivial k G -modules.

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