On soluble groups with finite homomorphic images of bounded rank
type: Item
instance of: scholarly article
title: On soluble groups with finite homomorphic images of bounded rank
zbMATH Open document ID: 0838.20040
DOI: 10.1007/BF02274668
author: A. V. Tushev
published in: Mathematical Notes
publication date: 1996-06-02T00:00:00Z
review text: Denote by \({\mathcal F}(K)\) the set of all finite homomorphic images of a group \(K\). A group is minimax if it has a finite subnormal series each factor of which satisfies either the minimality condition or maximality condition for subgroups. Let a finitely generated group \(G\) be the extension of a nilpotent group by an almost polycyclic group, and let \(H\) be a group of finite rank. The author proves that if \({\mathcal F}(G)\subseteq{\mathcal F}(H)\), then \(G\) is a minimax group. In particular, it is shown that if \(G\) is a finitely generated residually finite group, \(H\) is a soluble minimax group and \({\mathcal F}(G)\subseteq{\mathcal F}(H)\) then \(G\) is minimax.
Mathematics Subject Classification ID: 20F16
Mathematics Subject Classification ID: 20E26
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20F22
Mathematics Subject Classification ID: 20F14
zbMATH DE Number: 830760
zbMATH Keywords: finite homomorphic images
zbMATH Keywords: subnormal series
zbMATH Keywords: minimality condition
zbMATH Keywords: maximality condition
zbMATH Keywords: finitely generated groups
zbMATH Keywords: nilpotent groups
zbMATH Keywords: almost polycyclic groups
zbMATH Keywords: groups of finite rank
zbMATH Keywords: minimax groups
zbMATH Keywords: finitely generated residually finite groups
Wikidata QID: Q122270905
reviewed by: Alexander Ivanovich Budkin
MaRDI profile type: Publication
cites work: Q5654235
cites work: Q5182382
cites work: On the Finiteness of Certain Soluble Groups
cites work: Integral group rings of polycyclic-by-finite groups
full work available at URL: https://doi.org/10.1007/bf02274668
OpenAlex ID: W2061131369
description: scientific article; zbMATH DE number 830760