Groups with finitely many normalizers of subnormal subgroups.
type: Item
instance of: scholarly article
title: Groups with finitely many normalizers of subnormal subgroups.
zbMATH Open document ID: 1116.20020
author: Fausto De Mari
author: F. de Giovanni
published in: Journal of Algebra
publication date: 2006-12-07T00:00:00Z
review text: The authors study groups with finitely many normalizers of subnormal (respectively infinite subnormal) subgroups. Of course, if every subnormal subgroup is normal in a group \(G\) then \(G\) is a T-group (or a group in which normality is a transitive relation) and if every infinite subnormal subgroup is normal then \(G\) is called an IT-group [see \textit{S. Franciosi} and \textit{F. de Giovanni}, J. Algebra 96, 566-580 (1985; Zbl 0572.20016)]. Thus, generalizations of T- and IT-groups are considered in this article. The main results include: (1) Let \(G\) be a periodic soluble group with finitely many normalizers of infinite subnormal subgroups. Then \(G/\omega(G)\) is finite. (2) Let \(G\) be a soluble group with finitely many normalizers of subnormal subgroups. If \(G\) locally satisfies the maximal condition then \(G/\omega(G)\) is finite. Here \(\omega(G)\) denotes the Wielandt subgroup of \(G\).
reviewed by: Martyn Dixon
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20F16
zbMATH DE Number: 5078832
zbMATH Keywords: subnormal subgroups
zbMATH Keywords: normalizer subgroups
zbMATH Keywords: T-groups
zbMATH Keywords: transitive normality
zbMATH Keywords: soluble IT-groups
zbMATH Keywords: Wielandt subgroup
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2005.10.006
OpenAlex ID: W1980580787
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DOI: 10.1016/J.JALGEBRA.2005.10.006
description: scientific article; zbMATH DE number 5078832