A classification of fully residually free groups of rank three or less
type: Item
instance of: scholarly article
title: A classification of fully residually free groups of rank three or less
zbMATH Open document ID: 0899.20009
author: Benjamin Fine
author: Anthony Gaglione
author: Gerhard Rosenberger
author: Dennis Spellman
author: Alexei Myasnikov
published in: Journal of Algebra
publication date: 1998-09-09T00:00:00Z
review text: A group \(G\) is said to be fully residually free provided to every finite set \(S\) consisting of nontrivial elements there are a free group \(F\) and an homomorphism \(\varphi\colon G\to F\) such that every image \(\varphi(s)\), \(s\in S\) is nontrivial too. This property has been of great interest recently in terms of the study of questions in logic pertaining to certain other freeness properties in groups, and in connection with free tree actions. A group \(G\) is called \(n\)-free provided every subgroup of \(G\) generated by \(n\) elements is free. It is shown in the paper that every \(2\)-free residually free group is \(3\)-free. There are \(3\)-free fully residually free groups which are not \(4\)-free.
Mathematics Subject Classification ID: 20E05
Mathematics Subject Classification ID: 20E26
Mathematics Subject Classification ID: 20F10
Mathematics Subject Classification ID: 03C68
Mathematics Subject Classification ID: 20E08
zbMATH DE Number: 1139791
zbMATH Keywords: free groups
zbMATH Keywords: fully residually free groups
zbMATH Keywords: \(\Lambda\)-tree actions
zbMATH Keywords: freeness properties of groups
zbMATH Keywords: \(n\)-free groups
reviewed by: Vitaliĭ Roman'kov
MaRDI profile type: Publication
full work available at URL: jabr.1997.7205
OpenAlex ID: W2044463949
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DOI: 10.1006/JABR.1997.7205
description: scientific article; zbMATH DE number 1139791