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On primordial groups for the Green ring

Part of: Grothendieck groups and $K_0$ Representation theory of groups

Published online by Cambridge University Press:  24 October 2012

Alberto G. Raggi-Cárdenas  and
Nadia Romero
Alberto G. Raggi-Cárdenas
Affiliation:
Instituto de Matemáticas, Universidad Nacional Autónoma de México, AP 61-3, CP 58089, Morelia, Michoacán, Mexico ([email protected]; [email protected])
Nadia Romero
Affiliation:
Instituto de Matemáticas, Universidad Nacional Autónoma de México, AP 61-3, CP 58089, Morelia, Michoacán, Mexico ([email protected]; [email protected])
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Abstract

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Consider the Mackey functor that assigns to each finite group G the Green ring of finitely generated kG-modules, where k is a field of characteristic p > 0. Thévenaz foresaw in 1988 that the class of primordial groups for this functor is the family of k-Dress groups. In this paper we prove that this is true for the subfunctor defined by the Green ring of finitely generated kG-modules of trivial source.

Keywords

Green ringprimordial grouptrivial source module

MSC classification

Secondary: 20C05: Group rings of finite groups and their modules 19A22: Frobenius induction, Burnside and representation rings
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 56 , Issue 1 , February 2013 , pp. 337 - 347
Copyright
Copyright © Edinburgh Mathematical Society 2012

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