Groups whose proper subgroups are finite-by-nilpotent
type: Item
instance of: scholarly article
title: Groups whose proper subgroups are finite-by-nilpotent
zbMATH Open document ID: 0857.20015
DOI: 10.1007/BF01781552
author: Maoqian Xu
published in: Archiv der Mathematik
publication date: 1997-03-03T00:00:00Z
review text: The author considers non-finite-by-nilpotent groups with all proper subgroups finite-by-nilpotent; in short MNFN-groups. Finitely generated MNFN-groups \(G\) are perfect, with \(G/\Phi(G)\) infinite simple (Theorem 2.6); infinitely generated MNFN-groups belong to one of the following classes: (a) non-perfect MNFA-groups, (b) non-perfect MNN-groups with every subgroup subnormal, (c) locally nilpotent perfect MNN-groups (Theorem 3.5).
Mathematics Subject Classification ID: 20F19
Mathematics Subject Classification ID: 20F18
Mathematics Subject Classification ID: 20E15
zbMATH DE Number: 938546
zbMATH Keywords: minimal non-finite-by-nilpotent groups
zbMATH Keywords: finitely generated MNFN-groups
zbMATH Keywords: non-finite-by-nilpotent groups
zbMATH Keywords: proper subgroups finite-by-nilpotent
zbMATH Keywords: infinitely generated MNFN-groups
zbMATH Keywords: locally nilpotent perfect MNN-groups
reviewed by: Hermann Heineken
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01781552
OpenAlex ID: W14283623
description: scientific article; zbMATH DE number 938546