Groups with a bounded number of conjugacy classes of non-normal subgroups
type: Item
instance of: scholarly article
title: Groups with a bounded number of conjugacy classes of non-normal subgroups
zbMATH Open document ID: 0921.20042
author: Roberta La Haye
author: Akbar H. Rhemtulla
published in: Journal of Algebra
publication date: 1999-08-04T00:00:00Z
review text: Let \(G\) be a group, and let \(\nu(G)\) be the number of conjugacy classes of non-normal subgroups of \(G\). The authors prove that, if \(G\) is a finite group with \(\nu(G)\neq 0\), then the centre \(Z(G)\) of \(G\) contains a cyclic subgroup \(C\) of prime power order such that the order of \(G/C\) is the product of at most \(\nu(G)+1\) primes. A similar statement can also be obtained for infinite groups with finitely many conjugacy classes of non-normal subgroups, but the subgroup \(C\) must be a Prüfer group. Moreover, the authors give a description of infinite groups with finitely many conjugacy classes of non-normal subgroups, generalizing a previous result by \textit{R. Brandl, S. Franciosi} and the reviewer [Proc. R. Ir. Acad., Sect. A 95, No. 1, 17-27 (1995; Zbl 0851.20019)].
Mathematics Subject Classification ID: 20F24
zbMATH DE Number: 1275253
zbMATH Keywords: non-normal subgroups
zbMATH Keywords: conjugacy classes
MaRDI profile type: Publication
full work available at URL: jabr.1998.7690
OpenAlex ID: W1989686075
cites work: Finite groups in which the non-normal subgroups have nontrivial intersection
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cites work: Q4881258
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DOI: 10.1006/JABR.1998.7690
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description: scientific article; zbMATH DE number 1275253