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

Carlson, Jon and Mazza, Nadia and Thévenaz, Jacques (2013) Endotrivial modules over groups with quaternion or semi-dihedral Sylow 2-subgroup. Journal of the European Mathematical Society, 15 (1). pp. 157-177. ISSN 1435-9863

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Abstract

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 kG-modules, whose restrictions to P are isomorphic to the direct sum of the known exotic endotrivial kP-modules and some projective modules. This provides a description of the group T(G) of endotrivial kG-modules.