Automorphisms of free groups have finitely generated fixed point sets.

*(English)*Zbl 0628.20029As 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

##### 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
Full Text:
DOI

##### References:

[1] | \scD. Cooper, Dynamics of automorphisms of free groups, in preparation. |

[2] | \scS. Gersten, Fixed points of automorphisms of free groups, preprint. · Zbl 0616.20014 |

[3] | Dyer, J.L; Scott, G.P, Periodic automorphisms of free groups, Comm. algebra, 3, 195-201, (1975) · Zbl 0304.20029 |

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