Description of finite solvable minimal non-\({\mathcal F}\)-groups for an arbitrary totally local formation \({\mathcal F}\)
type: Item
instance of: scholarly article
title: Description of finite solvable minimal non-\({\mathcal F}\)-groups for an arbitrary totally local formation \({\mathcal F}\)
zbMATH Open document ID: 0684.20013
DOI: 10.1007/BF01139130
author: V. N. Semenchuk
published in: Mathematical Notes
publication date: 1988-01-01T00:00:00Z
review text: Let \({\mathcal M}({\mathcal F})\) be the set of all minimal non \({\mathcal F}\)-groups, i.e. groups not lying in some class of groups \({\mathcal F}\) all proper subgroups of which lie in \({\mathcal F}\). The paper describes solvable groups in \({\mathcal M}({\mathcal F})\) for an arbitrary totally local formation \({\mathcal F}\). It turns out that all such groups are two-generated. Special cases of this problem have been studied previously.
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D30
zbMATH DE Number: 4120385
zbMATH Keywords: minimal non \({\mathcal F}\)-groups
zbMATH Keywords: solvable groups
zbMATH Keywords: local formation
reviewed by: Rodica Covaci
MaRDI profile type: Publication
cites work: Note on $(LM)$-groups of finite orders
cites work: Extreme classes of finite soluble groups
cites work: Interpolation theorems in modal logics and amalgamable varieties of topological Boolean algebras
cites work: Q3961010
cites work: Nonsolvable finite groups all of whose local subgroups are solvable
description: scientific article; zbMATH DE number 4120385