Fixed points of automorphisms of free groups
type: Item
instance of: scholarly article
title: Fixed points of automorphisms of free groups
zbMATH Open document ID: 0616.20014
DOI: 10.1016/0001-8708(87)90004-1
published in: Advances in Mathematics
publication date: 1987-01-01T00:00:00Z
review text: The author gives a full proof of the theorem that the set of fixed points of an automorphism \(\phi\) of a finitely generated free group is a finitely generated subgroup. This was announced previously by him [Bull. Am. Math. Soc., New Ser. 8, 451-454 (1983; Zbl 0512.20014)] and settles in the affirmative a conjecture of G. P. Scott. Previously this was established in particular cases, for example in the case where \(\phi\) was of finite order or it was induced by a certain homeomorphism of the pair (M,x), where M is a compact bounded orientable two-manifold and \(x\in M\). For the proof he uses graphical representations of the automorphism, after he has written it as a product of Whitehead automorphisms, and then gives an algorithm to construct a finite set which generates the subgroup of fixed points of \(\phi\).
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 20E05
Mathematics Subject Classification ID: 20F28
zbMATH DE Number: 3998079
zbMATH Keywords: fixed points
zbMATH Keywords: automorphism
zbMATH Keywords: finitely generated free group
zbMATH Keywords: finitely generated subgroup
zbMATH Keywords: graphical representations
zbMATH Keywords: Whitehead automorphisms
author: Steve M. Gersten
MaRDI profile type: Publication
full work available at URL: 0001-8708(87)90004-1
OpenAlex ID: W2060941049
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description: scientific article; zbMATH DE number 3998079