Automorphisms of finite \(p\)-groups admitting a partition.

DOI10.1007/S10469-012-9189-2zbMath1264.20025OpenAlexW2094057237MaRDI QIDQ1928475

Eugenii I. Khukhro

Publication date: 3 January 2013

Published in: Algebra and Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10469-012-9189-2

zbMATH Keywords

finite \(p\)-groupsexponentnilpotency classpartitions of groupsunions of subgroupsHughes subgroupsplitting automorphismsderived lengthFrobenius groups of automorphismsautomorphisms of prime-power order

Mathematics Subject Classification ID

Arithmetic and combinatorial problems involving abstract finite groups (20D60) Special subgroups (Frattini, Fitting, etc.) (20D25) Automorphisms of abstract finite groups (20D45) Finite nilpotent groups, (p)-groups (20D15) Associated Lie structures for groups (20F40)

Related Items (4)

Rank and order of a finite group admitting a Frobenius group of automorphisms. ⋮ Lie algebras admitting a metacyclic Frobenius group of automorphisms ⋮ Finite groups and Lie rings with a metacyclic Frobenius group of automorphisms. ⋮ Some results of left and right α-commutators of groups

Cites Work

• Fixed points of the complements of Frobenius groups of automorphisms.
• Fixed points of Frobenius groups of automorphisms.
• Nilpotent groups and their automorphisms
• On the exponent of a finite group with an automorphism group of order twelve.
• The \(H_p\)-problem and the structure of \(H_p\)-groups
• Die Nilpotenz der \(H_ p\)-Gruppen
• Nilpotency of solvable groups admitting a splitting automorphism of prime order
• Frobenius groups as groups of automorphisms
• Frobenius groups of automorphisms and their fixed points
• Groups and Rings Having Automorphisms without Non-Trivial Fixed Elements
• Graded Lie rings with many commuting components and an application to 2-Frobenius groups
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