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arXiv · 1408.3982

The torsion group of endotrivial modules

Jon F. Carlson·Jacques Thévenaz
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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 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.

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Jon F. Carlson, Jacques Thévenaz. 2015-03-02. The torsion group of endotrivial modules. https://doi.org/10.2140/ant.2015.9.749

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