A cohomological criterion for p-nilpotence

DOI10.1016/0022-4049(71)90003-XzbMath0254.20038OpenAlexW2055222096MaRDI QIDQ2558388

Daniel Quillen

Publication date: 1972

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-4049(71)90003-x

Mathematics Subject Classification ID

Homological methods in group theory (20J05) Finite nilpotent groups, (p)-groups (20D15)

Related Items (30)

A \(p\)-nilpotency criterion. ⋮ Unnamed Item ⋮ The decomposition of the trivial module in the complexity quotient category ⋮ Carlson's theorem on varieties and transfer ⋮ On Carlson's conjecture for cohomology rings of modules ⋮ Varieties and modules with vanishing cohomology ⋮ Control of fusion by Abelian subgroups of the hyperfocal subgroup ⋮ Representations, resolutions and Quillen's dimension theorem ⋮ Frobenius operations and cohomology of gl₃ (F_q) ⋮ Dimensions of modules and their restrictions over modular group algebras ⋮ A note on the subgroup theorem in cohomological complexity theory ⋮ Quillen stratification for modules ⋮ Annihilators of cohomology modules ⋮ Group cohomology and control of \(p\)-fusion. ⋮ Complexity and varieties for infinitely generated modules, II ⋮ Varieties and elementary Abelian groups ⋮ The restriction map in cohomology of finite 2-groups ⋮ Spectrum of group cohomology and support varieties ⋮ Finite \(p\)-central groups of height \(k\). ⋮ Nilpotent \(p\)-local finite groups. ⋮ Another homological characterization of finite \(p\)-nilpotent groups ⋮ Equivariant BP-Cohomology for Finite Groups ⋮ Geometry of p-unipotent Lie algebras ⋮ Cohomological characterisations of finite solvable and nilpotent groups ⋮ Varieties and transfers ⋮ Cohomology of finite soluble groups ⋮ 𝑝-central groups and Poincaré duality ⋮ Complexity and elementary Abelian p-groups ⋮ The variety of an indecomposable module is connected ⋮ A Quillen stratification theorem for modules

Cites Work

• The \(p\)-period of a finite group
• Characters and cohomology of finite groups
• Nilpotent quotient groups
• The spectrum of an equivariant cohomology ring. I. II
• A Generalization of the Transfer Map in the Cohomology of Groups

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