#### 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 $\ell$-subgroups in any finite group of Lie type, for any prime $\ell$. 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