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

Jon F. CarlsonNadia MazzaJacques 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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