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Torsion-free endotrivial modules

Research output: Contribution to Journal/MagazineJournal articlepeer-review

<mark>Journal publication date</mark>15/01/2014
<mark>Journal</mark>Journal of Algebra
Number of pages21
Pages (from-to)413-433
Publication StatusPublished
Early online date15/02/13
<mark>Original language</mark>English


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.