Normalizers of nilpotent residuals
type: Item
instance of: scholarly article
title: Normalizers of nilpotent residuals
zbMATH Open document ID: 1386.20011
author: Lü Gong
author: I. M. Isaacs
published in: Archiv der Mathematik
publication date: 2017-02-24T00:00:00Z
review text: Let \(G\) be a finite group. \textit{L. Gong} et al. [J. Algebra Appl. 15, No. 1, Article ID 1650008, 9 p. (2016; Zbl 1342.20017)] have noted that if a subgroup \(M\) of \(G\) normalises the derived subgroup of every non-subnormal subgroup of \(G\), then \(M\) does not necessarily normalises the derived subgroup of every subgroup. On the other hand, the authors prove the following. If a subgroup \(M\) of \(G\) normalises the nilpotent (soluble) residual of every non-subnormal subgroup of \(G\), then \(M\) normalises the nilpotent (soluble) residual of every subgroup. The authors ask whether the analogous result holds for supersolvable residuals, this question has been answered affirmatively by \textit{A. Ballester-Bolinches} et al. [Arch. Math. 109, No. 4, 305--310 (2017; Zbl 1378.20017)].
reviewed by: János Kurdics
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D35
Mathematics Subject Classification ID: 20D15
zbMATH DE Number: 6688680
zbMATH Keywords: finite group
zbMATH Keywords: soluble residual
zbMATH Keywords: supersoluble residual
zbMATH Keywords: nilpotent residual
zbMATH Keywords: formation
zbMATH Keywords: residual
zbMATH Keywords: subnormal group
MaRDI profile type: Publication
full work available at URL: s00013-016-0995-y
OpenAlex ID: W2555768085
cites work: On the generalized norm of a finite group.
cites work: Endliche Gruppen I
cites work: Q3521460
DOI: 10.1007/S00013-016-0995-Y
description: scientific article; zbMATH DE number 6688680