Nilpotency of solvable groups admitting a splitting automorphism of prime order

DOI10.1007/BF01669107zbMath0475.20018MaRDI QIDQ1159762

Eugenii I. Khukhro

Publication date: 1980

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

Full work available at URL: https://eudml.org/doc/187087

zbMATH Keywords

lower central seriessplitting automorphismsolvability lengthnilpotency length

Mathematics Subject Classification ID

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

Related Items

Finite \(p\)-groups admitting an automorphism of order \(p\) with a small number of fixed points, On groups with an interval isomorphic to a projective geometry, On groups with a splitting automorphism of prime order, Splittable groups with splitting component of prime index, Fitting height of finite groups admitting a fixed-point-free automorphism satisfying an additional polynomial identity, Automorphisms of finite \(p\)-groups admitting a partition., Finite groups admitting a coprime automorphism satisfying an additional polynomial identity, Nilpotency in varieties of groups with operators, On groups with a normal splitting component, On a generalization of the Hughes subgroup, On the centralizer and the commutator subgroup of an automorphism., Infinite groups containing a proper Hughes subgroup \(H_3(G)\), Splitting automorphisms of free Burnside groups, Almost regular automorphisms, Splitting automorphisms of order \(p^k\) of free Burnside groups are inner.

Cites Work

• Die Nilpotenz der \(H_ p\)-Gruppen
• Groups and Rings Having Automorphisms without Non-Trivial Fixed Elements
• On the Finiteness of Certain Soluble Groups
• On the H p -Problem for Finite p-Groups
• Solution of the Hughes Problem for Finite p-Groups of Class 2p - 2
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