Finite groups with an automorphism of prime order whose centralizer has small rank.

DOI10.1016/j.jalgebra.2006.02.039zbMath1108.20019OpenAlexW2062818653MaRDI QIDQ855703

Victor D. Mazurov, Eugenii I. Khukhro

Publication date: 7 December 2006

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2006.02.039

zbMATH Keywords

regular automorphismsrankspowerful \(p\)-groupsalmost nilpotent groupsHall-Higman-type theorems

Mathematics Subject Classification ID

Automorphisms of abstract finite groups (20D45)

Related Items (16)

Finite groups with ℋ-subgroups or strongly closed subgroups ⋮ Exponent of a finite group admitting a coprime automorphism of prime order ⋮ FINITE GROUPS WITH ENGEL SINKS OF BOUNDED RANK ⋮ Unnamed Item ⋮ Rank and order of a finite group admitting a Frobenius group of automorphisms. ⋮ On the rank of a finite group of odd order with an involutory automorphism ⋮ Finite groups with a soluble group of coprime automorphisms whose fixed points have bounded Engel sinks ⋮ Almost Engel compact groups ⋮ Compact groups in which all elements are almost right Engel ⋮ Large characteristic subgroups satisfying multilinear commutator identities. ⋮ Automorphisms of prime order almost regular in the sense of rank. ⋮ Engel sinks of fixed points in finite groups ⋮ Centralizer of Engel Elements in a Group ⋮ Unnamed Item ⋮ Almost Engel finite and profinite groups ⋮ Rank and order of a finite group admitting a Frobenius-like group of automorphisms.

Cites Work

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• Powerful \(p\)-groups. I: Finite groups.
• On characters and fixed points of coprime operator groups
• Finite \(p\)-groups admitting an automorphism of order \(p\) with a small number of fixed points
• Finite soluble groups containing an element of prime order whose centralizer is small
• Automorphisms and Fitting factors of finite groups
• On orders of finite groups and centralizers of \(p\)-elements
• Involutory automorphisms of finite groups and their centralizers
• Finite soluble and nilpotent groups with a restriction on the rank of the centralizer of an automorphism of prime order
• On groups in which every subgroup is subnormal
• On finite soluble groups
• Strong finiteness conditions in locally finite groups
• Groups and Rings Having Automorphisms without Non-Trivial Fixed Elements
• FINITE GROUPS WITH FIXED-POINT-FREE AUTOMORPHISMS OF PRIME ORDER
• LIE RINGS AND LIE GROUPS ADMITTING AN ALMOST REGULAR AUTOMORPHISM OF PRIME ORDER
• On the number of generators of a finite group
• Automorphisms of solvable groups

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