Automorphisms of free groups have finitely generated fixed point sets
type: Item
instance of: scholarly article
title: Automorphisms of free groups have finitely generated fixed point sets
zbMATH Open document ID: 0628.20029
DOI: 10.1016/0021-8693(87)90229-8
author: Daryl Cooper
published in: Journal of Algebra
publication date: 1987-01-01T00:00:00Z
review text: As the title indicates this paper deals with the problem of the subgroup of the fixed points of an automorphism of a free group. It was first proved by \textit{S. Gersten} [Adv. Math. 64, 51-85 (1987; Zbl 0616.20014)] that the subgroup of fixed points of an automorphism of a finitely generated free group is finitely generated settling thus a conjecture of G. P. Scott. In the present paper the author gives a new proof based on new ideas. More precisely the author considers the end completion of the free group F (the set of infinite reduced words for a suitable metric), he studies the homeomorphism induced on this completion by the given automorphism and proves first the analogous result for the fixed set of this homeomorphism.
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 20E05
Mathematics Subject Classification ID: 20F28
zbMATH DE Number: 4021441
zbMATH Keywords: automorphism
zbMATH Keywords: subgroup of fixed points
zbMATH Keywords: finitely generated free group
zbMATH Keywords: end completion
zbMATH Keywords: homeomorphism
MaRDI profile type: Publication
full work available at URL: 0021-8693(87)90229-8
OpenAlex ID: W2076181847
cites work: Fixed points of automorphisms of free groups
cites work: Periodic automorphisms of free groups
description: scientific article; zbMATH DE number 4021441