Groups of infinite rank with a locally finite term in the lower central series.
type: Item
instance of: scholarly article
title: Groups of infinite rank with a locally finite term in the lower central series.
zbMATH Open document ID: 1331.20042
author: F. de Giovanni
author: M. Trombetti
published in: Beiträge zur Algebra und Geometrie
publication date: 2015-10-16T00:00:00Z
review text: A group \(G\) is called strongly locally graded, if every finitely generated nontrivial subgroup of any quotient group \(H/K\) contains a proper subgroup of finite index. The authors prove: If \(G\) is a strongly locally graded group of infinite rank and all proper subgroups of infinite rank of \(G\) are (locally finite)-by-nilpotent [(locally finite)-by-(locally nilpotent)], then so is \(G\) itself. (So here subgroups of finite rank need not be considered.)
reviewed by: Hermann Heineken
Mathematics Subject Classification ID: 20F14
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20E25
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20F19
zbMATH DE Number: 6495597
zbMATH Keywords: groups of infinite Prüfer rank
zbMATH Keywords: strongly locally graded groups
zbMATH Keywords: subgroups of finite index
zbMATH Keywords: (locally finite)-by-(locally nilpotent) groups
MaRDI profile type: Publication
full work available at URL: s13366-014-0207-5
OpenAlex ID: W1977181235
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DOI: 10.1007/S13366-014-0207-5
description: scientific article; zbMATH DE number 6495597