Monomorphisms of finitely generated free groups have finitely generated equalizers
type: Item
instance of: scholarly article
title: Monomorphisms of finitely generated free groups have finitely generated equalizers
zbMATH Open document ID: 0582.20023
DOI: 10.1007/BF01388804
author: Richard Z. Goldstein
author: Edward C. Turner
published in: Inventiones Mathematicae
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143287
review text: If \(\phi\),\(\psi\) : \(G\to H\) are homomorphisms of groups, then the subgroup \(Eq(\phi,\psi)=\{x|\) \(\phi (x)=\psi (x)\}\) of G is called the equalizer of \(\phi\) and \(\psi\). The main result, which takes care of a conjecture of Stallings, is the following: If \(\phi\) and \(\psi\) are monomorphisms and G is a finitely generated free group, then Eq(\(\phi\),\(\psi)\) is finitely generated. The authors use graphical methods and prove all the main results in the 3-dimensional Whitehead model. They mention that \textit{J. Stallings} [Graphical Theory of automorphisms of Free Groups, Proc. Alto Conf. Comb. Group Theory] and \textit{D. Cooper} [Automorphisms of free groups have f.g. fixed point sets (preprint)] have also given a proof of this main result.
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 20E05
zbMATH DE Number: 3931255
zbMATH Keywords: homomorphisms of groups
zbMATH Keywords: equalizer
zbMATH Keywords: monomorphisms
zbMATH Keywords: finitely generated free group
MaRDI profile type: Publication
cites work: Fixed points of automorphisms of free groups
cites work: Automorphisms of free groups and their fixed points
cites work: On Automorphisms of Free Groups I
cites work: Topology of finite graphs
cites work: Q3755639
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description: scientific article; zbMATH DE number 3931255