An embedding theorem for certain residually finite groups
type: Item
instance of: scholarly article
title: An embedding theorem for certain residually finite groups
zbMATH Open document ID: 0862.20024
DOI: 10.1007/BF01195232
author: John S. Wilson
author: Pavel Zalesskij
published in: Archiv der Mathematik
publication date: 1997-05-20T00:00:00Z
review text: A group \(G\) is said to be cyclic subgroup separable (or css for short) if for each cyclic subgroup \(C\) and each element \(g\) of \(G\) not lying in \(C\), there is a normal subgroup \(U\) of finite index in \(G\) such that \(g\) is not in \(CU\). The authors prove that every countable css group can be embedded in a \(2\)-generator css group.
Mathematics Subject Classification ID: 20E26
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 938592
zbMATH Keywords: residually finite groups
zbMATH Keywords: subgroup separable groups
zbMATH Keywords: subgroups of finite index
zbMATH Keywords: 2-generator css groups
reviewed by: Alexander Ivanovich Budkin
MaRDI profile type: Publication
cites work: A free product of finitely generated nilpotent groups amalgamating a cycle that is not subgroup separable
cites work: Residually finite hnn extensions
cites work: Some remarks on profinite HNN extensions
cites work: Q4114528
cites work: Embedding Theorems for Groups
cites work: Q4145882
cites work: Conjugacy separability of amalgamated free products of groups
cites work: An example of a non-LERF group which is a free product of LERF groups with an amalgamated cyclic subgroup
cites work: Residual finiteness of a class of knot groups
cites work: Two Examples of Soluble Groups that are not Conjugacy Separable
full work available at URL: https://doi.org/10.1007/bf01195232
OpenAlex ID: W1964620711
description: scientific article; zbMATH DE number 938592