Finite \(p\)-groups admitting an automorphism of order \(p\) with a small number of fixed points

DOI10.1007/BF01157528zbMath0598.20024MaRDI QIDQ1079656

Eugenii I. Khukhro

Publication date: 1985

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

zbMATH Keywords

fixed pointsfinite \(p\)-groupsregular automorphismsnilpotent groupsnilpotent lengthsautomorphisms of order \(p\)

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)

Related Items (12)

Almost solubility of Lie algebras with almost regular automorphisms ⋮ Finite groups with an automorphism of prime order whose centralizer has small rank. ⋮ Unnamed Item ⋮ Counterexamples to a rank analog of the Shepherd-Leedham-Green-McKay theorem on finite \(p\)-groups of maximal nilpotency class. ⋮ Lie rings with almost regular automorphisms. ⋮ Locally finite groups containing a \(2\)-element with Chernikov centralizer. ⋮ Finite groups and Lie rings with a metacyclic Frobenius group of automorphisms. ⋮ On finite soluble groups with almost fixed-point-free automorphisms of noncoprime order. ⋮ Finite 𝑝-groups with a Frobenius group of automorphisms whose kernel is a cyclic 𝑝-group ⋮ On almost regular automorphisms of finite \(p\)-groups ⋮ Unnamed Item ⋮ Construction of finite p-groups that admit partitions

Cites Work

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• On a special class of \(p\)-groups
• Periodic groups in which the centralizer of an involution has bounded order
• Space groups and groups of prime-power order. I
• Nilpotency of solvable groups admitting a splitting automorphism of prime order
• Groups and Rings Having Automorphisms without Non-Trivial Fixed Elements
• Automorphisms of Solvable Groups
• ON p-GROUPS OF MAXIMAL CLASS I

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