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The slice Burnside ring and the section Burnside ring of a finite group

Published online by Cambridge University Press:  22 March 2012

Serge Bouc*
Affiliation:
CNRS-LAMFA, Université de Picardie, 33 rue St Leu, 80039, Amiens cedex 1, France (email: [email protected])
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Abstract

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This paper introduces two new Burnside rings for a finite group G, called the slice Burnside ring and the section Burnside ring. They are built as Grothendieck rings of the category of morphisms of G-sets and of Galois morphisms of G-sets, respectively. The well-known results on the usual Burnside ring, concerning ghost maps, primitive idempotents, and description of the prime spectrum, are extended to these rings. It is also shown that these two rings have a natural Green biset functor structure. The functorial structure of unit groups of these rings is also discussed.

Type
Research Article
Copyright
Copyright © Foundation Compositio Mathematica 2012

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