Carlson, Jon and Mazza, Nadia and Thevenaz, Jacques (2014) Torsion-free endotrivial modules. Journal of Algebra, 398. pp. 413-433. ISSN 0021-8693
Full text not available from this repository.Abstract
Let $G$ be a finite group and let $T(G)$ be the abelian group of equivalence classes of endotrivial $kG$-modules, where $k$ is an algebraically closed field of characteristic~$p$. We investigate the torsion-free part $TF(G)$ of the group $T(G)$ and look for generators of~$TF(G)$. We describe three methods for obtaining generators. Each of them only gives partial answers to the question but we obtain more precise results in some specific cases. We also conjecture that $TF(G)$ can be generated by modules belonging to the principal block and we prove the conjecture in some cases.