The functor of units of Burnside rings for \(p\)-groups

DOI10.4171/CMH/103zbMath1142.19001arXivmath/0607703OpenAlexW2951577613MaRDI QIDQ2466957

Serge Bouc

Publication date: 17 January 2008

Published in: Commentarii Mathematici Helvetici (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607703

zbMATH Keywords

Burnside ringunitbiset functorDade group

Mathematics Subject Classification ID

Modular representations and characters (20C20) Frobenius induction, Burnside and representation rings (19A22) Units, groups of units (associative rings and algebras) (16U60)

Related Items (27)

The slice Burnside ring and the section Burnside ring of a finite group ⋮ Borel-Smith functions and the Dade group ⋮ A ghost algebra of the double Burnside algebra in characteristic zero ⋮ On the unit group of the Burnside ring as a biset functor for some solvable groups ⋮ Gluing endo-permutation modules ⋮ Genotypes of irreducible representations of finite \(p\)-groups ⋮ Representations of finite groups. Abstracts from the workshop held March 25--31, 2012. ⋮ The Whitehead group of (almost) extra-special \(p\)-groups with \(p\) odd ⋮ The Brauer group of Burnside rings ⋮ Orthogonal units of the bifree double Burnside ring ⋮ Tornehave morphisms. III: The reduced tornehave morphism and the Burnside unit functor. ⋮ The Roquette category of finite \(p\)-groups ⋮ Embeddings and units of Burnside rings ⋮ Unit groups of representation rings and their ghost rings as inflation functors ⋮ Orthogonal units of the double Burnside ring ⋮ Categorical constructions related to finite groups ⋮ Rhetorical biset functors, rational \(p\)-biset functors and their semisimplicity in characteristic zero ⋮ Fibered biset functors ⋮ Alcahestic subalgebras of the alchemic algebra and a correspondence of simple modules ⋮ Tornehave morphisms. II: The lifted Tornehave morphism and the dual of the Burnside functor ⋮ Rational \(p\)-biset functors ⋮ Multiplicative induction and units for the ring of monomial representations ⋮ A functorial presentation of units of Burnside rings ⋮ Tornehave Morphisms I: Resurrecting the Virtual Permutation Sets Annihilated by Linearization ⋮ Burnside rings of fusion systems and their unit groups ⋮ The table of marks, the Kostka matrix, and the character table of the symmetric group ⋮ Some simple biset functors

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