Torsion free endotrivial modules for finite groups of Lie type

Carlson, Jon F. and Grodal, Jesper and Mazza, Nadia and Nakano, Daniel K. (2022) Torsion free endotrivial modules for finite groups of Lie type. Pacific Journal of Mathematics, 317 (2). pp. 239-274. ISSN 0030-8730

Text (TF_final)
TF_final.pdf - Accepted Version
Available under License Creative Commons Attribution.
Download (444kB)

Abstract

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