Coclass and cohomology.

DOI10.1016/j.jpaa.2005.01.001zbMath1105.20044OpenAlexW1981951115MaRDI QIDQ2483829

Carlson, Jon F.

Publication date: 1 August 2005

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

Full work available at URL: https://doi.org/10.1016/j.jpaa.2005.01.001

zbMATH Keywords

finite \(p\)-groupscohomology ringsspectral sequencescohomology of groupscoclass\(p\)-adic uniserial space groups

Mathematics Subject Classification ID

Cohomology of groups (20J06) Finite nilpotent groups, (p)-groups (20D15)

Related Items (12)

Cohomology of uniserial \(p\)-adic space groups with cyclic point group ⋮ Cohomological periodicities of crystallographic groups. ⋮ The origins of coclass theory ⋮ Computing a spectral sequence of finite Heisenberg groups of prime power order ⋮ Cohomology of \(p\)-groups of nilpotency class smaller than \(p\) ⋮ Spectral sequences via examples ⋮ COMPUTATION OF LOW-DIMENSIONAL (CO)HOMOLOGY GROUPS FOR INFINITE SEQUENCES OF p-GROUPS WITH FIXED COCLASS ⋮ Cohomology of finite \(p\)-groups of fixed nilpotency class ⋮ Cohomological uniqueness of some p-groups ⋮ The isomorphism problem for graded algebras and its application to \(\mathrm{mod-}p\) cohomology rings of small \(p\)-groups. ⋮ The Quillen categories of \(p\)-groups and coclass theory. ⋮ Cohomology of uniserial 𝑝-adic space groups

Uses Software

• Magma

Cites Work

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• Some remarks on Sylow subgroups of general linear groups
• The structure of finite \(p\)-groups: Effective proof of the coclass conjectures
• Gröbner bases and the computation of group cohomology.
• Cohomology rings of finite groups. With an appendix: Calculations of cohomology rings of groups of order dividing 64.
• Space Groups and Groups of Prime-Power Order, V. A Bound to the Dimension of Space Groups with Fixed Coclass
• Classifying 2-groups by coclass
• The Structure of Finite p -Groups
• 𝑝-central groups and Poincaré duality
• Space Groups and Groups of Prime Power Order VI. a Bound to the Dimension of a 2-Adic Space Group with Fixed Coclass
• Cohomology of uniformly powerful $p$-groups

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