Algebra & Number Theory

The torsion group of endotrivial modules

Jon Carlson and 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.

Article information

Source
Algebra Number Theory, Volume 9, Number 3 (2015), 749-765.

Dates
Received: 5 November 2014
Revised: 28 January 2015
Accepted: 27 February 2015
First available in Project Euclid: 16 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.ant/1510842317

Digital Object Identifier
doi:10.2140/ant.2015.9.749

Mathematical Reviews number (MathSciNet)
MR3340550

Zentralblatt MATH identifier
1325.20006

Subjects
Primary: 20C20: Modular representations and characters

Keywords
modular representation theory

Citation

Carlson, Jon; Thévenaz, Jacques. The torsion group of endotrivial modules. Algebra Number Theory 9 (2015), no. 3, 749--765. doi:10.2140/ant.2015.9.749. https://projecteuclid.org/euclid.ant/1510842317


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