TY - JOUR

T1 - Torsion-free endotrivial modules

AU - Carlson, Jon

AU - Mazza, Nadia

AU - Thevenaz, Jacques

PY - 2014/1/15

Y1 - 2014/1/15

N2 - 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.

AB - 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.

KW - endotrivial modules

KW - Modular representations of finite groups

U2 - 10.1016/j.jalgebra.2013.01.020

DO - 10.1016/j.jalgebra.2013.01.020

M3 - Journal article

VL - 398

SP - 413

EP - 433

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -