Examples of retracts in free groups that are not the fixed subgroup of any automorphism.
type: Item
instance of: scholarly article
title: Examples of retracts in free groups that are not the fixed subgroup of any automorphism.
zbMATH Open document ID: 1035.20018
DOI: 10.1016/S0021-8693(03)00535-0
published in: Journal of Algebra
publication date: 2003-12-04T00:00:00Z
review text: For a free group \(F_n\) of rank \(n\), the relationship between the family of subgroups fixed by an endomorphism of \(F_n\) and the family of subgroups fixed by an automorphism of \(F_n\) is studied. An infinite sequence of explicit examples of retracts of \(F_n\) is constructed (i.e., subgroups \(H\) whose identity map extends to a homomorphism from \(F_n\) to \(H\), so these are in particular fixed subgroups of an endomorphism of \(F_n\)) which are not fixed subgroups of any automorphism of \(F_n\).
Mathematics Subject Classification ID: 20E05
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 2013038
zbMATH Keywords: free groups
zbMATH Keywords: fixed subgroups of automorphisms
zbMATH Keywords: retracts
zbMATH Keywords: fixed subgroups of endomorphisms
author: Armando Martino
author: Enric Ventura Capell
reviewed by: Bruno Zimmermann
MaRDI profile type: Publication
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full work available at URL: s0021-8693(03)00535-0
OpenAlex ID: W2128039523
description: scientific article; zbMATH DE number 2013038