JournalsjemsVol. 15, No. 1pp. 157–177

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

  • Jon F. Carlson

    University of Georgia, Athens, United States
  • Nadia Mazza

    Lancaster University, UK
  • Jacques Thévenaz

    Ecole Polytechnique Fédérale de Lausanne, Switzerland
Endotrivial modules over groups with quaternion or semi-dihedral Sylow 2-subgroup cover
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Abstract

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

Cite this article

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. 157–177

DOI 10.4171/JEMS/358