Finite groups with \(f\)-abnormal or \(f\)-subnormal subgroups
type: Item
instance of: scholarly article
title: Finite groups with \(f\)-abnormal or \(f\)-subnormal subgroups
zbMATH Open document ID: 0835.20029
DOI: 10.1007/BF02110358
author: V. N. Semenchuk
published in: Mathematical Notes
publication date: 1995-09-27T00:00:00Z
review text: A formation \(f\) is said to be an \(\check S\)-formation if each finite solvable minimal non-\(f\)-group is either a Shmidt group or a group of prime order. The paper contains a new characterization of solvable local hereditary \(\check S\)-formations. One proves that a hereditary local solvable formation \(f\) is an \(\check S\)-formation if and only if \(f\) contains each group \(G=AB\), where \(A\) and \(B\) are \(f\)-subnormal \(f\)- subgroups of the group \(G\). Making use of this result, the author obtains a description of finite groups for which any proper subgroup is either \(f\)-subnormal or \(f\)-abnormal for an arbitrary hereditary solvable \(\check S\)-formation.
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D40
zbMATH DE Number: 797878
zbMATH Keywords: finite solvable minimal non-\(f\)-groups
zbMATH Keywords: Shmidt groups
zbMATH Keywords: groups of prime order
zbMATH Keywords: solvable local hereditary \(\check S\)-formations
zbMATH Keywords: \(f\)-subnormal \(f\)-subgroups
zbMATH Keywords: finite groups
zbMATH Keywords: \(f\)-abnormal subgroups
reviewed by: Rodica Covaci
MaRDI profile type: Publication
cites work: Q3994689
cites work: Q3970804
cites work: Q3031165
cites work: Groups with only normal and abnormal subgroups
cites work: A note on subnormal and abnormal chains
cites work: Q3803323
cites work: Interpolation theorems in modal logics and amalgamable varieties of topological Boolean algebras
cites work: Q3961010
Recommended article: Q3803323
Recommended article: Finite groups with abnormal and \(\mathfrak{U}\)-subnormal subgroups
Recommended article: Q3597667
Recommended article: Finite groups with only \({\mathfrak{F}}\)-normal and \({\mathfrak{F}}\)-abnormal subgroups
Recommended article: Finite groups with σ-abnormal or 𝔉-subnormal σ-primary subgroups
Recommended article: Finite groups with \(\mathfrak{F}\)-subnormal subgroups
Recommended article: Q5744044
Recommended article: Finite groups with abnormal or formational subnormal primary subgroups
Recommended article: Finite groups with σ-abnormal or σ-subnormal σ-primary subgroups
Recommended article: Finite groups all of whose subgroups are σ-subnormal or σ-abnormal
description: scientific article; zbMATH DE number 797878