A solvable group admitting a regular splitting automorphism of prime order is nilpotent

DOI10.1007/BF01673828zbMath0426.20027MaRDI QIDQ1135931

Eugenii I. Khukhro

Publication date: 1979

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

Full work available at URL: https://eudml.org/doc/187031

zbMATH Keywords

soluble groupinfinite Frobenius groupsregular splitting automorphism

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Solvable groups, supersolvable groups (20F16) Nilpotent groups (20F18) Automorphisms of infinite groups (20E36)

Related Items (13)

Equality problem for center-by-metabelian Lie algebras ⋮ Relative linear dependence problem for the variety \({\mathfrak AN}_ {\mathbf{c}}\) of Lie algebras ⋮ The occurrence problem for Lie algebras ⋮ The word problem for subvarieties of the variety \({\mathfrak N}_ 2{\mathfrak A}\) ⋮ Subalgebras of finitely defined Lie algebras ⋮ The word problem in a variety of groups containing N//2A ⋮ On solvable Lie algebras with one defining relation ⋮ New results in the theory of associative and Lie rings ⋮ On groups with a Frobenius element ⋮ Letter to the editor ⋮ Polynilpotent Lie algebras given by one defining relation ⋮ The equality problem and free products of Lie algebras and of associative algebras ⋮ Metabelian binary-Lie algebras

Cites Work

• The \(H_p\)-problem and the structure of \(H_p\)-groups
• Die Nilpotenz der \(H_ p\)-Gruppen
• Some aspects of groups with unique roots
• Groups and Rings Having Automorphisms without Non-Trivial Fixed Elements
• FINITE GROUPS WITH FIXED-POINT-FREE AUTOMORPHISMS OF PRIME ORDER
• On the Finiteness of Certain Soluble Groups
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