The functor of rational representations for \(p\)-groups.

DOI10.1016/j.aim.2003.08.002zbMath1055.20005OpenAlexW2004287657MaRDI QIDQ1877879

Serge Bouc

Publication date: 19 August 2004

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aim.2003.08.002

zbMATH Keywords

finite \(p\)-groupsGrothendieck groupsrational representationscategories of finitely generated modulesbiset functorslattices of subfunctors

Mathematics Subject Classification ID

Ordinary representations and characters (20C15) 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

Borel-Smith functions and the Dade group ⋮ Genotypes of irreducible representations of finite \(p\)-groups ⋮ The Roquette category of finite \(p\)-groups ⋮ Composition factors of functors ⋮ The uncountable lattice of all subfunctors of the functor of rational representations ⋮ Categorical constructions related to finite groups ⋮ Rhetorical biset functors, rational \(p\)-biset functors and their semisimplicity in characteristic zero ⋮ Stabilizing bisets ⋮ Endo-\(p\)-permutation modules. ⋮ A filtration of the modular representation functor ⋮ Alcahestic subalgebras of the alchemic algebra and a correspondence of simple modules ⋮ Rational \(p\)-biset functors ⋮ Biset functors and genetic sections for \(p\)-groups ⋮ The Dade group of a \(p\)-group.

Cites Work

• Unnamed Item
• Realisierung von Darstellungen endlicher nilpotenter Gruppen. (Realization of representations of finite-dimensional nilpotent groups)
• Set functors equipped with a double action
• The group of endo-permutation modules
• A remark on a theorem of Ritter and Segal
• Tensor induction of relative syzygies