On infinitely generated groups whose proper subgroups are solvable.

DOI10.1016/j.jalgebra.2013.11.001zbMath1304.20053OpenAlexW2066675296MaRDI QIDQ397899

A. O. Asar

Publication date: 12 August 2014

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2013.11.001

zbMATH Keywords

finitely generated subgroupstorsion-free groupsperiodic groupshomomorphic imagesresidually nilpotent groupsnormal closuresinfinitely generated groupsminimal non-soluble groups

Mathematics Subject Classification ID

Periodic groups; locally finite groups (20F50) Generators, relations, and presentations of groups (20F05) Generalizations of solvable and nilpotent groups (20F19) Residual properties and generalizations; residually finite groups (20E26) Local properties of groups (20E25)

Related Items

On minimal non-(residually nilpotent) locally graded groups ⋮ Unnamed Item ⋮ Unnamed Item

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Locally finite groups with all subgroups either subnormal or nilpotent-by-Chernikov.
• On Fitting \(p\)-groups with all proper subgroups satisfying an outer commutator law.
• Groups whose proper subgroups are Baer-by-Chernikov or Baer-by-(finite rank).
• Barely transitive permutation groups
• Torsionsfreie Gruppen, deren Untergruppen alle subnormal sind. (Torsion free groups all of whose subgroups are subnormal)
• Torsionsgruppen, deren Untergruppen alle subnormal sind. (Torsion groups all subgroups of which are subnormal)
• A first course in group theory
• On the normalizer condition and barely transitive permutation groups
• Hypercentral groups with all subgroups subnormal
• Locally finite minimal non-FC-groups
• Locally Nilpotent p -Groups whose Proper Subgroups are Hypercentral or Nilpotent-by-Chernikov
• Large characteristic subgroups satisfying multilinear commutator identities
• Characterizations of minimal non-solvable Fitting p-groups