The Dade group of a \(p\)-group.

DOI10.1007/s00222-005-0476-6zbMath1099.20004OpenAlexW1981459973MaRDI QIDQ2491157

Serge Bouc

Publication date: 26 May 2006

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00222-005-0476-6

zbMATH Keywords

Dade groupsendo-permutation modulesfinite \(p\)-groupssimple modulesBurnside ringsrational representationsmodular representation theoryendo-trivial modulesbiset functorsgenetic sections

Mathematics Subject Classification ID

Modular representations and characters (20C20) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Finite nilpotent groups, (p)-groups (20D15) Frobenius induction, Burnside and representation rings (19A22)

Related Items (38)

Borel-Smith functions and the Dade group ⋮ Connected components of the category of elementary Abelian \(p\)-subgroups. ⋮ Gluing endo-permutation modules ⋮ The Dade group of Mackey functors for \(p\)-groups ⋮ Representations of finite groups. Abstracts from the workshop held March 25--31, 2012. ⋮ Dade groups for finite groups and dimension functions ⋮ The Whitehead group of (almost) extra-special \(p\)-groups with \(p\) odd ⋮ Basic Morita equivalences and isotypies ⋮ Modular representations of finite groups with trivial restriction to Sylow subgroups. ⋮ On the lifting of the Dade group ⋮ Tornehave morphisms. III: The reduced tornehave morphism and the Burnside unit functor. ⋮ Brauer relations in finite groups ⋮ A tour of \(p\)-permutation modules and related classes of modules ⋮ The Roquette category of finite \(p\)-groups ⋮ The Dade group of a finite group. ⋮ Simple biset functors and double Burnside ring ⋮ Lifting endo-\(p\)-permutation modules ⋮ Strong fusion control and stable equivalences. ⋮ Toward a classification of endotrivial modules ⋮ Categorical constructions related to finite groups ⋮ Rhetorical biset functors, rational \(p\)-biset functors and their semisimplicity in characteristic zero ⋮ A ghost ring for the left-free double Burnside ring and an application to fusion systems ⋮ Endo-\(p\)-permutation modules. ⋮ Endotrivial modules for finite group schemes ⋮ Fibered \(p\)-biset functor structure of the fibered Burnside rings ⋮ 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 ⋮ The crossed Burnside ring, the Drinfel'd double, and the Dade group of a \(p\)-group ⋮ Rational \(p\)-biset functors ⋮ Monomial Modules and Endo-Monomial Modules ⋮ A sectional characterization of the Dade group ⋮ A functorial presentation of units of Burnside rings ⋮ The Dade group of a fusion system ⋮ Tornehave Morphisms I: Resurrecting the Virtual Permutation Sets Annihilated by Linearization ⋮ Relations between permutation representations in positive characteristic ⋮ Vertices of Lie modules. ⋮ Equivalences between blocks of cohomological Mackey algebras. ⋮ Some simple biset functors

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