The mod-p cohomology rings of some p-groups

DOI10.1017/S0305004100070766zbMath0782.20042arXiv0711.4831MaRDI QIDQ4034720

Ian J. Leary

Publication date: 16 May 1993

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0711.4831

zbMATH Keywords

central extensionsintegral cohomologyrestrictionsmod-\(p\) cohomology rings

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Cohomology of groups (20J06) Finite nilpotent groups, (p)-groups (20D15) Serre spectral sequences (55T10)

Related Items (28)

ModpCohomology Algebra of Special Linear Group ⋮ Depth and transfer maps in the cohomology of groups ⋮ \(3\)-groups are not determined by their integral cohomology rings ⋮ The spectral sequence of a split extension and the cohomology of an extraspecial group of order \(p^ 3\) and exponent \(p\) ⋮ Chern classes and extraspecial groups ⋮ The group of endotrivial modules in the normal case. ⋮ Representations of the double Burnside algebra and cohomology of the extraspecial \(p\)-group ⋮ On the cohomology of pro-fusion systems ⋮ A family of finitep‐groups satisfying Carlson's depth conjecture ⋮ Cohomology classes of the \(Qd (p)\) groups ⋮ Cohomology classes of \(Qd(3)\) ⋮ Chow rings of nonabelian \(p\)-groups of order \(p^{3}\) ⋮ Representations of the double Burnside algebra and cohomology of the extraspecial \(p\)-group. II. ⋮ Essential cohomology and extraspecial $p$-groups ⋮ Elementary abelian \({p}\)-groups are the only finite groups with the Borsuk-Ulam property ⋮ On third homologies of groups and of quandles via the Dijkgraaf-Witten invariant and Inoue-Kabaya map ⋮ Free actions of finite groups on $S^n \times S^n$ ⋮ Chern classes and the extraspecialp-group of orderp⁵and exponentp ⋮ THE INTEGRAL COHOMOLOGY OF SOMEp-GROUPS ⋮ Nilpotency degree of cohomology rings in characteristic 3 ⋮ Cohomological uniqueness of some p-groups ⋮ Constructing endotrivial modules. ⋮ On odd degree parts of cohomology of sporadic simple groups whose Sylow \(p\)-subgroup is the extra-special \(p\)-group of order \(p^3\) ⋮ The \(K(n)\)-Euler characteristic of extraspecial \(p\)-groups ⋮ Hochschild-Serre spectral sequences of split extensions and cohomology of some extra-special \(p\)-groups ⋮ All 𝑝-local finite groups of rank two for odd prime 𝑝 ⋮ Hochschild cohomology ring of the modular group ⋮ A counterexample to the Ch(G)-conjecture

Cites Work

• The mod p cohomology rings of the nonabelian split metacyclic p-groups
• Perturbation theory and free resolutions for nilpotent groups of class 2
• Cohomology of nilpotent groups of class 2
• Matric Massey products
• Massey Higher Products
• The Integral Cohomology Rings of Groups of Order p 3

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