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Torsion-free endotrivial modules

Research output: Contribution to journalJournal article

Published

Journal publication date15/01/2014
JournalJournal of Algebra
Volume398
Number of pages21
Pages413-433
Early online date15/02/13
Original languageEnglish

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.