Groups with subnormality for all subgroups that are not finitely generated
type: Item
instance of: scholarly article
title: Groups with subnormality for all subgroups that are not finitely generated
zbMATH Open document ID: 0848.20023
DOI: 10.1007/BF01759354
published in: Annali di Matematica Pura ed Applicata. Serie Quarta
publication date: 1996-10-27T00:00:00Z
review text: Groups in which every subgroup is subnormal have been studied extensively. The idea here is to study groups in which `most' of the subgroups are subnormal and the authors consider groups in which every subgroup which is not finitely generated is subnormal. They call these groups \(db\)-groups, being `dual' to Baer groups in which every finitely generated subgroup is subnormal. All groups with Max are \(db\)-groups including infinite simple groups with Max. To avoid these the authors restrict attention to locally finite groups and radical groups. An infinite locally finite \(db\)-group possessing non-subnormal subgroups is a Chernikov group and a complete description is given for this case. The main part of the paper leads to a satisfactory description of the radical \(db\)-groups.
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20F19
Mathematics Subject Classification ID: 20F50
zbMATH DE Number: 878430
zbMATH Keywords: subnormal subgroups
zbMATH Keywords: locally finite groups
zbMATH Keywords: radical groups
zbMATH Keywords: non-subnormal subgroups
zbMATH Keywords: Chernikov groups
zbMATH Keywords: radical \(db\)-groups
author: Hermann Heineken
author: L. A. Kurdachenko
reviewed by: M. J. Tomkinson
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01759354
OpenAlex ID: W1992057154
description: scientific article; zbMATH DE number 878430