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Growth and order of automorphisms of free groups and free Burnside groups

Rémi Coulon and Arnaud Hilion

Geometry & Topology 21 (2017) 1969–2014

We prove that an outer automorphism of the free group is exponentially growing if and only if it induces an outer automorphism of infinite order of free Burnside groups with sufficiently large odd exponent.

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automorphism groups, free groups, Burnside groups, growth of automorphisms, train-track theory
Mathematical Subject Classification 2010
Primary: 20E05, 20E36, 20F28, 20F50, 20F65
Secondary: 68R15
Received: 15 October 2013
Revised: 10 May 2016
Accepted: 6 September 2016
Published: 19 May 2017
Proposed: Martin Bridson
Seconded: Walter Neumann, Jean-Pierre Otal
Rémi Coulon
Institut de Recherche Mathématique de Rennes - UMR 6625
CNRS - Université de Rennes 1
Campus de Beaulieu, bâtiments 22 et 23
263 avenue du Général Leclerc, CS 74205
35042 Rennes Cedex
Arnaud Hilion
I2M UMR 7373 - Centre de Mathématiques et Informatique
Aix Marseille Université
CNRS, Centrale Marseille, I2M, Marseille, France
Technopôle Château-Gombert
39, rue F Joliot Curie
13453 Marseille 13