More countably recognizable classes of groups.
type: Item
instance of: scholarly article
title: More countably recognizable classes of groups.
zbMATH Open document ID: 1172.20029
author: J. Martínez
published in: Journal of Pure and Applied Algebra
publication date: 2009-04-16T00:00:00Z
review text: A class \(\mathcal C\) of groups is countably recognizable if \(G\in\mathcal C\) for every group \(G\) that has all countable subgroups lying in \(\mathcal C\). \textit{R. Baer} [in the article Math. Z. 79, 344-363 (1962; Zbl 0105.25901)] introduced countable recognizability. Series of articles continued its investigation. \textit{M. R. Dixon, M. J. Evans} and \textit{H. Smith} [in the paper J. Group Theory 10, No. 5, 641-653 (2007; Zbl 1129.20018)] proved that certain important class extensions are countably recognizable. In the interesting article under review, the author proves that certain classes of groups that are either (locally soluble)-by-finite rank or finite rank-by-(locally soluble) are countably recognizable.
Mathematics Subject Classification ID: 20F19
Mathematics Subject Classification ID: 20E25
Mathematics Subject Classification ID: 20E10
zbMATH DE Number: 5544386
zbMATH Keywords: (locally soluble)-by-finite rank groups
zbMATH Keywords: countably recognizable groups
zbMATH Keywords: countable subgroups
zbMATH Keywords: classes of groups
reviewed by: Igor Subbotin
MaRDI profile type: Publication
full work available at URL: j.jpaa.2008.11.030
OpenAlex ID: W2029830734
cites work: Abzählbar erkennbare gruppentheoretische Eigenschaften
cites work: Some countably recognizable classes of groups
cites work: Q5662114
cites work: Q5654236
cites work: A remark on products of locally soluble groups
cites work: Subclasses of locally Minimax Groups Closed under Normal Joins
cites work: Residually finite groups of finite rank
cites work: Q4040041
DOI: 10.1016/J.JPAA.2008.11.030
description: scientific article; zbMATH DE number 5544386