Let be a finite group with a Sylow 2-subgroup which is either quaternion or semi-dihedral. Let be an algebraically closed field of characteristic 2. We prove the existence of exotic endotrivial -modules, whose restrictions to are isomorphic to the direct sum of the known exotic endotrivial -modules and some projective modules. This provides a description of the group of endotrivial -modules.
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Jon F. Carlson, Nadia Mazza, Jacques Thévenaz, Endotrivial modules over groups with quaternion or semi-dihedral Sylow 2-subgroup. J. Eur. Math. Soc. 15 (2013), no. 1, pp. 157–177DOI 10.4171/JEMS/358