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## Torsion free endotrivial modules for finite groups of Lie type

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Journal publication date 18/03/2022 Pacific Journal of Mathematics Accepted/In press English

### 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.