The normalizer property for integral group rings of finite solvable T-groups

DOI10.1515/jgt.2011.105zbMath1254.16030OpenAlexW2031078975MaRDI QIDQ2903540

Zheng Xing Li, Jin Ke Hai

Publication date: 10 August 2012

Published in: jgth (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/jgt.2011.105

zbMATH Keywords

finite groupswreath productssemidirect productssubnormal subgroupsgroups of unitssolvable groupsintegral group ringscentral unitsnormalizer propertycyclic Sylow subgroups

Mathematics Subject Classification ID

Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Group rings (16S34) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Subnormal subgroups of abstract finite groups (20D35) Units, groups of units (associative rings and algebras) (16U60)

Related Items (7)

Class-preserving coleman automorphisms of permutational wreath products with 2-closed base groups ⋮ The influence of maximal quotient groups on the normalizer conjecture of integral group rings ⋮ Integral group rings with all central units trivial ⋮ Coleman automorphisms of permutational wreath products II ⋮ Coleman automorphisms of holomorphs of finite abelian groups. ⋮ Class-Preserving Coleman Automorphisms of Finite Groups with Prescribed Centralizers ⋮ Coleman automorphisms of generalized dihedral groups.

Cites Work

• Group automorphisms inducing the identity map on cohomology
• The normalizer of a group in the unit group of its group ring
• Coleman automorphisms of finite groups.
• Class-preserving Coleman automorphisms of finite groups
• The normalizer property for integral group rings of Frobenius groups
• The normalizer of a metabelian group in its 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 Wreath Products of Finite Nilpotent Groups by Cyclic Groups
• Automorphisms of Finite Groups
• On the normalizer property for integral group rings
• Automorphisms of finite groups
• The Normalizer Property for Integral Group Rings of Complete Monomial Groups
• A counterexample to the isomorphism problem for integral group rings
• Class-preserving automorphisms of finite groups
• Local analysis of the normalizer problem

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