Cooper, Daryl Automorphisms of free groups have finitely generated fixed point sets. (English) Zbl 0628.20029 J. Algebra 111, 453-456 (1987). 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 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. Reviewer: S.Andreadakis Cited in 6 ReviewsCited in 45 Documents MSC: 20E36 Automorphisms of infinite groups 20E05 Free nonabelian groups 20F28 Automorphism groups of groups Keywords:automorphism; subgroup of fixed points; finitely generated free group; end completion; homeomorphism Citations:Zbl 0616.20014 PDFBibTeX XMLCite \textit{D. Cooper}, J. Algebra 111, 453--456 (1987; Zbl 0628.20029) Full Text: DOI References: [3] Dyer, J. L.; Scott, G. P., Periodic automorphisms of free groups, Comm. Algebra, 3, 195-201 (1975) · Zbl 0304.20029 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.