Vol. 317, No. 2, 2022

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Torsion free endotrivial modules for finite groups of Lie type

Jon F. Carlson, Jesper Grodal, Nadia Mazza and Daniel K. Nakano

Vol. 317 (2022), No. 2, 239–274
Abstract

We determine the torsion free rank of the group of endotrivial modules for any finite group of Lie type, in both defining and nondefining characteristic. Equivalently, we classify the maximal rank 2 elementary abelian -subgroups in any finite group of Lie type, for any prime . This classification may be of independent interest.

Keywords
endotrivial modules, elementary abelian subgroups, finite groups of Lie type
Mathematical Subject Classification
Primary: 20C20, 20C33
Secondary: 20E15
Milestones
Received: 12 August 2021
Revised: 16 December 2021
Accepted: 18 March 2022
Published: 14 July 2022
Authors
Jon F. Carlson
Department of Mathematics
University of Georgia
Department of Mathematics
Athens, GA
United States
Jesper Grodal
Department of Mathematical Sciences
University of Copenhagen
Copenhagen
Denmark
Nadia Mazza
Department of Mathematics and Statistics
University of Lancaster
Lancaster
United Kingdom
Daniel K. Nakano
Department of Mathematics
University of Georgia
Athens, GA
United States