Finite soluble and nilpotent groups with a restriction on the rank of the centralizer of an automorphism of prime order

DOI10.1007/BF02674608zbMath0956.20013OpenAlexW2076122821MaRDI QIDQ1586971

Eugenii I. Khukhro

Publication date: 21 November 2000

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/225018

zbMATH Keywords

finite solvable groupsFitting subgroupsfinite nilpotent groupsalmost regular automorphismsautomorphisms of prime order

Mathematics Subject Classification ID

Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Automorphisms of abstract finite groups (20D45) Finite nilpotent groups, (p)-groups (20D15)

Related Items (3)

Finite groups with an automorphism of prime order whose centralizer has small rank. ⋮ Large characteristic subgroups satisfying multilinear commutator identities. ⋮ Automorphisms of prime order almost regular in the sense of rank.

Cites Work

• On orders of finite groups and centralizers of \(p\)-elements
• Involutory automorphisms of finite groups and their centralizers
• On groups in which every subgroup is subnormal
• On finite soluble groups
• Groups and Rings Having Automorphisms without Non-Trivial Fixed Elements
• FINITE GROUPS WITH FIXED-POINT-FREE AUTOMORPHISMS OF PRIME ORDER
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