Fixed points of Frobenius groups of automorphisms.

DOI10.1134/S1064562411020050zbMath1238.20038MaRDI QIDQ656269

Natalia Yu. Makarenko, Eugenii I. Khukhro, P. V. Shumyatskij

Publication date: 17 January 2012

Published in: Doklady Mathematics (Search for Journal in Brave)

zbMATH Keywords

Lie algebrasexponentsFrobenius groups of automorphismsnilpotency classesrank of finite groups

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Automorphisms of abstract finite groups (20D45) Finite nilpotent groups, (p)-groups (20D15) Lie (super)algebras associated with other structures (associative, Jordan, etc.) (17B60) Associated Lie structures for groups (20F40)

Related Items (15)

Rank and order of a finite group admitting a Frobenius group of automorphisms. ⋮ Lie algebras admitting a metacyclic Frobenius group of automorphisms ⋮ Automorphisms of finite \(p\)-groups admitting a partition. ⋮ On the influence of fixed point free nilpotent automorphism groups ⋮ Fitting height of a finite group with a Frobenius group of automorphisms. ⋮ On groups and Lie algebras admitting a Frobenius group of automorphisms. ⋮ Finite groups and Lie rings with a metacyclic Frobenius group of automorphisms. ⋮ Double automorphisms of graded Lie algebras ⋮ Exponent of a finite group with a fixed-point-free four-group of automorphisms. ⋮ Frobenius groups of automorphisms with almost fixed point free kernel ⋮ Action of a Frobenius-like group. ⋮ Exponent of a finite group with a four-group of automorphisms. ⋮ Finite 𝑝-groups with a Frobenius group of automorphisms whose kernel is a cyclic 𝑝-group ⋮ On the exponent of a finite group with an automorphism group of order twelve. ⋮ Rank and order of a finite group admitting a Frobenius-like group of automorphisms.

Cites Work

• Unnamed Item
• Powerful \(p\)-groups. I: Finite groups.
• Automorphisms of finite groups of bounded rank
• Bounding the exponent of a finite group with automorphisms
• Centralizers of finite nilpotent subgroups in locally finite groups
• Frobenius groups as groups of automorphisms
• Graded Lie rings with many commuting components and an application to 2-Frobenius groups
• Sur les groupes nilpotents et les anneaux de Lie

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