Group automorphisms inducing the identity map on cohomology

DOI10.1016/0022-4049(87)90028-4zbMath0624.20024OpenAlexW2070184701MaRDI QIDQ1092163

Stefan Jackowski, Zbigniew S. Marciniak

Publication date: 1987

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(87)90028-4

zbMATH Keywords

inner automorphismscohomologyconnected Lie groupAtiyah spectral sequencefinite solvablenormal Sylow 2-subgroup

Mathematics Subject Classification ID

Homological methods in group theory (20J05) Automorphisms of infinite groups (20E36) Linear algebraic groups over the reals, the complexes, the quaternions (20G20) Cohomology theory for linear algebraic groups (20G10)

Related Items (44)

Automorphisms of Finite Groups ⋮ On the normalizer property for integral group rings ⋮ Unnamed Item ⋮ Coleman automorphisms of finite groups and their minimal normal subgroups ⋮ The normalizer property for integral group rings of finite solvable T-groups ⋮ The Normalizer Property for Integral Group Rings of Some Finite Nilpotent-by-Nilpotent Groups ⋮ On the normaliser problem for G-adapted group rings of torsion groups ⋮ Outer group automorphisms may become inner in the integral group ring ⋮ The influence of maximal quotient groups on the normalizer conjecture of integral group rings ⋮ On Coleman automorphisms of finite nilpotent groups by cyclic groups ⋮ The modular isomorphism problem: a survey ⋮ Class-preserving Coleman automorphisms of finite groups whose Sylow 2-subgroups are semidihedral ⋮ Homomorphisms and rigid isomorphisms of twisted group doubles ⋮ The normalizer property for integral group rings of holomorphs of finite nilpotent groups and the symmetric groups ⋮ Normalizer property of finite groups with almost simple subgroups ⋮ Coleman automorphisms of permutational wreath products II ⋮ The normalizer property for the integral group ring of the wreath product of two symmetric groups S_k and S_n ⋮ Isomorphisms of integral group rings of infinite groups ⋮ Coleman automorphisms of finite groups with a self-centralizing normal subgroup ⋮ On Coleman automorphisms of wreath products of finite nilpotent groups by Abelian groups. ⋮ Class-preserving automorphisms and inner automorphisms of certain tree products of groups. ⋮ On the normalizers of the unitary subgroup in an integral group ring ⋮ The normalizer property for integral group rings of wreath products of finite nilpotent groups by some 2-groups ⋮ The normalizer property for integral group rings of holomorphs of finite groups with trivial center ⋮ The Normalizer Property for Integral Group Rings of a Class of Complete Monomial Groups ⋮ COLEMAN AUTOMORPHISMS OF STANDARD WREATH PRODUCTS OF NILPOTENT GROUPS BY GROUPS WITH PRESCRIBED SYLOW 2-SUBGROUPS ⋮ The normalizer property of integral group rings of semidirect products of finite 2-closed groups by rational groups ⋮ The Normalizer Property for Integral Group Rings of Complete Monomial Groups ⋮ On hypercentral units in integral group rings ⋮ Local analysis of the normalizer problem ⋮ The normalizer property for finite groups whose Sylow 2-subgroups are abelian ⋮ On the normalizer problem. ⋮ Units of \(p\)-power order in principal \(p\)-blocks of \(p\)-constrained groups ⋮ Coleman automorphisms of holomorphs of finite abelian groups. ⋮ The Normalizer Property for Integral Group Rings of Wreath Products of Finite Nilpotent Groups by Cyclic Groups ⋮ Coleman Automorphisms of Permutational Wreath Products ⋮ The Subgroup Normalizer Problem for Integral Group Rings of Some Nilpotent and Metacyclic Groups ⋮ Class preserving automorphisms of Blackburn groups ⋮ The normalizer of a group in the unit group of its group ring ⋮ The normalizer property for integral group rings of Frobenius groups ⋮ The normalizer of a metabelian group in its integral group ring ⋮ On the normalizer problem for integral group rings of torsion groups ⋮ Class-Preserving Coleman Automorphisms of Finite Groups with Prescribed Centralizers ⋮ Class-preserving Coleman automorphisms of some classes of finite groups

Cites Work

• Characters and cohomology of finite groups
• Group homomorphisms inducing isomorphisms of cohomology
• The spectrum of an equivariant cohomology ring. I. II
• Observations on group rings
• On the Modular Group Ring of a p-Group
• Endliche Gruppen I
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

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