THE TORSION GROUP OF ENDOTRIVIAL MODULES

JON F. CARLSON AND JACQUES THEVENAZ

Abstract. Let G be a finite group and let T(G) be the abelian group of equiv- 
alence classes of endotrivial kG-modules, where k is an algebraically closed field 
of characteristic p. We determine, in terms of the structure of G, the kernel of 
the restriction map from T(G) to T(S), where S is a Sylow p-subgroup of G, in 
the case when S is abelian. This provides a classification of all torsion endotrivial 
kG-modules in that case.