Torsion-free endotrivial modules
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.