Cohomology of split group extensions

DOI10.1016/0021-8693(74)90099-4zbMath0277.20071OpenAlexW4212932804MaRDI QIDQ1393494

Chih-Han Sah

Publication date: 1974

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0021-8693(74)90099-4

Mathematics Subject Classification ID

Cohomology of groups (20J06) Homological methods in group theory (20J05) Extensions, wreath products, and other compositions of groups (20E22)

Related Items

A Moufang loop, the exceptional Jordan algebra, and a cubic form in 27 variables ⋮ Cohomology of split group extensions and characteristic classes. ⋮ On the cohomology of algebraic and related finite groups ⋮ Automorphisms of descending mod-\(p\) central series ⋮ Automorphisms of group extensions and differentials in the Lyndon-Hochschild-Serre spectral sequence ⋮ Invariants of \(\mathbb{Z}/p\)-homology 3-spheres from the abelianization of the level-\(p\) mapping class group ⋮ A seven-term exact sequence for the cohomology of a group extension. ⋮ On cohomology of crystallographic groups with cyclic holonomy of split type. ⋮ Representations of \(SL_n\) over finite local rings of length two ⋮ Infinite groups ⋮ Characteristic classes for cohomology of split Hopf algebra extensions ⋮ Automorphisms of \(p\)-compact groups and their root data ⋮ 1-cohomologies of a special linear group with coefficients in a module of truncated polynomials ⋮ On the homology of split extensions with $p$–elementary kernel ⋮ A gerbe for the elliptic gamma function ⋮ Cohomology of Metacyclic Groups ⋮ Linear groups of degree at most 27 over residue rings modulo \(p^k\). ⋮ The inverse deformation problem ⋮ Cohomology of split group extensions. II ⋮ Finite groups of order \(2^a3^b13^c\) ⋮ On the cohomology of the finite special linear groups. I, II ⋮ Reflection fusion categories ⋮ WZW orientifolds and finite group cohomology ⋮ The second degree cohomology of finite orthogonal groups. I ⋮ Braided Picard groups and graded extensions of braided tensor categories ⋮ Exact sequences in the cohomology of a group extension ⋮ Some 3-transposition cohomology ⋮ Change of rings and characteristic classes ⋮ Invertibility of linear maps preserving matrix invariants ⋮ A structure theorem for subgroups of $GL_n$ over complete local Noetherian rings with large residual image ⋮ A generalization of Sankaran and LVMB manifolds

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Solution of the congruence subgroup problem for \(\text{SL}_ n\) \((n\geq 3)\) and \(\text{Sp}_{2n}\) \((n\geq 2)\)
• Seminar on algebraic groups and related finite groups. Held at the Institute for Advanced Study, Princeton/N.J., 1968/69
• Irreducible modular representations of finite Chevalley groups
• Representations of Algebraic Groups
• The Eichler Cohomology Groups and Automorphic Forms
• The Cohomology of Group Extensions
• Characteristic Classes for Modules Over Groups. I
• Introduction to Algebraic K-Theory. (AM-72)
• Cohomology of Group Extensions
• Les Isomorphismes Exceptionnels Entre Les Groupes Classiques Finis
• On a class of doubly transitive groups
• Automorphisms of finite groups
• Groups of cohomological dimension one