Groups with a maximality condition for some non-normal subgroups
type: Item
instance of: scholarly article
title: Groups with a maximality condition for some non-normal subgroups
zbMATH Open document ID: 0835.20039
DOI: 10.1007/BF01266319
author: Giovanni Cutolo
author: L. A. Kurdachenko
published in: Geometriae Dedicata
publication date: 1996-04-10T00:00:00Z
review text: Many authors have considered groups satisfying the minimal or the maximal condition on the set of subgroups which do not satisfy a property \(\mathcal P\). In particular [\textit{G. Cutolo}, Riv. Mat. Pura Appl. 9, 49-59 (1991; Zbl 0751.20022)] groups with the maximal condition on the set of non- normal subgroups are investigated, and this condition is equivalent to the maximal condition on the set of finitely generated non-normal subgroups. In this article the authors consider groups satisfying the maximal condition on the set of non-normal subgroups which are not finitely generated. The main theorem of the paper concerns the classification of generalized soluble groups with this property. As a corollary a description is obtained of generalized soluble groups in which every non-normal subgroup is finitely generated. The special case of nilpotent groups with this property was already considered in the above quoted paper by Cutolo.
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20F16
Mathematics Subject Classification ID: 20E34
zbMATH DE Number: 806236
zbMATH Keywords: maximal condition on sets of nonnormal subgroups
zbMATH Keywords: finitely generated non- normal subgroups
zbMATH Keywords: generalized soluble groups
reviewed by: Silvana Franciosi
MaRDI profile type: Publication
cites work: Fast-Polyminimaxgruppen
cites work: Polyminimaxgruppen
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cites work: Q3941589
cites work: Q5593854
cites work: Q5628342
cites work: Modules over nilpotent groups of finite rank
cites work: Monomial characters and normal subgroups of finite groups
full work available at URL: https://doi.org/10.1007/bf01266319
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description: scientific article; zbMATH DE number 806236