On some groups whose subnormal subgroups are contranormal-free
type: Item
instance of: scholarly article
title: On some groups whose subnormal subgroups are contranormal-free
author: L. A. Kurdachenko
author: P. Longobardi
author: M. Maj
published in: International Journal of Group Theory
publication date: 2024-10-16T00:00:00Z
review text: \textit{J. S. Rose} [Math. Z. 106, 97--112 (1968; Zbl 0169.03402)] introduced the concept of contranormal subgroups. These are defined as subgroups whose normal closure is the entire group. In this interesting article, the authors explore groups which have no contranormal subgroups, referring to them as ``contranormal-free''. Clearly, a finite group is nilpotent if and only if it is contranormal-free. The authors here study the infinite groups whose subnormal subgroups are contranormal-free groups, presenting many interesting and technical results, some of which describe the Baer groups. For example, they prove the following as a corollary of their main results:\N\NLet \(G\) be a periodic solvable group. If every subnormal subgroup of \(G\) is contranormal-free, then \(G\) is a Baer group.
reviewed by: Kıvanç Ersoy
Mathematics Subject Classification ID: 20F19
Mathematics Subject Classification ID: 20E34
Mathematics Subject Classification ID: 20F12
zbMATH DE Number: 7927533
zbMATH Keywords: contranormal subgroups
zbMATH Keywords: subnormal subgroups
zbMATH Keywords: nilpotent groups
zbMATH Keywords: hypercentral groups
zbMATH Keywords: upper central series, Baer group, contranormal-free groups
MaRDI profile type: Publication
DOI: 10.22108/IJGT.2024.139136.1871
description: scientific article; zbMATH DE number 7927533