Groups whose non-subnormal subgroups have a transitive normality relation.
type: Item
instance of: scholarly article
title: Groups whose non-subnormal subgroups have a transitive normality relation.
zbMATH Open document ID: 1043.20016
author: F. de Giovanni
author: Alessio Russo
author: Giovanni Vincenzi
published in: Bulletin of the Brazilian Mathematical Society. New Series
publication date: 2003-01-01T00:00:00Z
review text: The authors consider groups whose non-subnormal subgroups are T-groups and whose subnormal subgroups are of bounded defect or of unrestricted defect. They call a group \(G\) \(k\)-metahamiltonian if every nonabelian subgroup of \(G\) is subnormal with defect at most \(k\). In the case that there is no restriction to the defect examples of results are the following: If \(G\) is nontrivial and locally finite, then \(G\) contains a nontrivial normal Sylow subgroup (Theorem 2.8), if \(G\) is finitely generated and soluble, then \(G\) is nilpotent or Abelian-by-finite (Lemma 2.9), if \(G\) is hyper-(locally (soluble-by-finite)), then \(G\) is soluble and locally nilpotent or of derived length 4 (Theorem 2.10). If the defect is bounded by \(k\), we have if \(G\) is locally soluble, it is \(k\)-metahamiltonian (Theorem 3.5).
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20F22
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 2016641
zbMATH Keywords: T-groups
zbMATH Keywords: non-subnormal subgroups
zbMATH Keywords: Sylow subgroups
reviewed by: Hermann Heineken
MaRDI profile type: Publication
full work available at URL: s00574-003-0009-0
OpenAlex ID: W2086930163
DOI: 10.1007/S00574-003-0009-0
description: scientific article; zbMATH DE number 2016641