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The classification of endotrivial modules
 Invent. Math
"... Abstract. Let G be a finite group and let T (G) be the abelian group of equivalence classes of endotrivial kGmodules, where k is an algebraically closed field of characteristic p. We investigate the torsionfree part TF (G) of the group T (G) and look for generators of TF (G). We describe three met ..."
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Abstract. Let G be a finite group and let T (G) be the abelian group of equivalence classes of endotrivial kGmodules, where k is an algebraically closed field of characteristic p. We investigate the torsionfree 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. 1.
doi:10.1112/blms/bdr006 On simple endotrivial modules
"... R. Robinson We show that when G is a finite group that contains an elementary Abelian subgroup of order p2 and k is an algebraically closed field of characteristic p, then the study of simple endotrivial kGmodules that are not monomial may be reduced to the case when G is quasisimple. 1. ..."
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R. Robinson We show that when G is a finite group that contains an elementary Abelian subgroup of order p2 and k is an algebraically closed field of characteristic p, then the study of simple endotrivial kGmodules that are not monomial may be reduced to the case when G is quasisimple. 1.