Finite soluble groups admitting an automorphism of prime power order with few fixed points

DOI10.1017/S0305004100067487zbMath0629.20007MaRDI QIDQ3765964

Brian Hartley, Volker Turau

Publication date: 1987

Published in: Mathematical Proceedings of the Cambridge Philosophical Society (Search for Journal in Brave)

zbMATH Keywords

fixed pointsFitting seriesfinite soluble groupcyclic automorphism groupcritical subgroupSylow r-subgroup

Mathematics Subject Classification ID

Finite solvable groups, theory of formations, Schunck classes, Fitting classes, (pi)-length, ranks (20D10) Sylow subgroups, Sylow properties, (pi)-groups, (pi)-structure (20D20) Arithmetic and combinatorial problems involving abstract finite groups (20D60) Special subgroups (Frattini, Fitting, etc.) (20D25) Automorphisms of abstract finite groups (20D45)

Related Items (9)

A four group of automorphisms with a small number of fixed points ⋮ Unnamed Item ⋮ Finite groups admitting a coprime automorphism satisfying an additional polynomial identity ⋮ Locally finite groups containing a \(2\)-element with Chernikov centralizer. ⋮ On characters and fixed points of coprime operator groups ⋮ Finite Groups and Lie Rings with an Automorphism of Order 2ⁿ ⋮ On finite soluble groups with almost fixed-point-free automorphisms of noncoprime order. ⋮ On finite groups admitting a special noncoprime action ⋮ Almost regular automorphisms

Cites Work

• Unnamed Item
• Fitting height of groups and of fixed points
• Solvable groups admitting an automorphism of prime power order whose centralizer is small
• Finite soluble groups containing an element of prime order whose centralizer is small
• Supersolvable automorphism groups of solvable groups.
• On groups in which every subgroup is subnormal
• Groups admitting a fixed-point-free automorphism of order \(2^ n\)
• Solvable Groups Admitting a Fixed-Point-Free Automorphism of Prime Power Order
• Endliche Gruppen I

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