Endotrivial modules for finite groups of Lie type A in nondefining characteristic

Carlson, Jon and Mazza, Nadia and Nakano, Daniel (2016) Endotrivial modules for finite groups of Lie type A in nondefining characteristic. Mathematische Zeitschrift, 282 (1). pp. 1-24. ISSN 0025-5874

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Abstract

Let $G$ be a finite group such that $\SL(n,q)\subseteq G \subseteq \GL(n,q)$ and $Z$ be a central subgroup of $G$. In this paper we determine the group $T(G/Z)$ consisting of the equivalence classes of endotrivial $k(G/Z)$-modules where $k$ is an algebraically closed field of characteristic $p$ such that $p$ does not divide $q$. The results in this paper complete the classification of endotrivial modules for all finite groups of (untwisted) Lie Type $A$, initiated earlier by the authors.