Generalizing Baer's norm
type: Item
instance of: scholarly article
title: Generalizing Baer's norm
zbMATH Open document ID: 1441.20010
author: Mark L. Lewis
author: Mohammad Zarrin
published in: Journal of Group Theory
publication date: 2019-01-09T00:00:00Z
review text: Let \(G\) be a group and \(n\) a positive integer. The authors define \(B_n(G)\) to be the intersection of the normalizers of all the non-\(n\)-subnormal subgroups of \(G\). They give a new characterization for nilpotent groups in terms of a series defined via \(B_n(G)\). The authors also prove the following interesting result: Theorem 1.1. If \(G\) is a finite group and \(n\) is a positive integer, then there is a positive integer \(m\) so that \(B_n(G)\) is contained in \(Z_m(G)\) (the \(n\)-th term of the upper central series).
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20D35
Mathematics Subject Classification ID: 20D30
Mathematics Subject Classification ID: 20F14
zbMATH DE Number: 6998944
zbMATH Keywords: finite nilpotent groups
zbMATH Keywords: subnormal subgroups
zbMATH Keywords: Baer norm
zbMATH Keywords: upper central series
zbMATH Keywords: normalizers
reviewed by: Igor Subbotin
MaRDI profile type: Publication
full work available at URL: jgth-2018-0031
OpenAlex ID: W2887536612
cites work: Q4756764
cites work: Group Elements of Prime Power Index
cites work: Alternate proof of the Reinhold Baer theorem on 2-groups with nonabelian norm.
cites work: Endliche Gruppen I
cites work: On groups in which every subgroup is subnormal
cites work: Non-subnormal subgroups of groups.
Wikidata QID: Q129380499
DOI: 10.1515/JGTH-2018-0031
description: scientific article; zbMATH DE number 6998944