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

Rémi Coulon; Arnaud Hilion

doi:10.2140/gt.2017.21.1969

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Home > Journals > Geom. Topol. > Volume 21 > Issue 4 > Article

2017 Growth and order of automorphisms of free groups and free Burnside groups

Rémi Coulon, Arnaud Hilion

Geom. Topol. 21(4): 1969-2014 (2017). DOI: 10.2140/gt.2017.21.1969

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Abstract

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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Rémi Coulon. Arnaud Hilion. "Growth and order of automorphisms of free groups and free Burnside groups." Geom. Topol. 21 (4) 1969 - 2014, 2017. https://doi.org/10.2140/gt.2017.21.1969

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Received: 15 October 2013; Revised: 10 May 2016; Accepted: 6 September 2016; Published: 2017

First available in Project Euclid: 19 October 2017

zbMATH: 06726515

MathSciNet: MR3654102

Digital Object Identifier: 10.2140/gt.2017.21.1969

Subjects:

Primary: 20E05 , 20E36 , 20F28 , 20F50 , 20F65

Secondary: 68R15

Keywords: automorphism groups , Burnside groups , ‎free groups , growth of automorphisms , train-track theory

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Rémi Coulon, Arnaud Hilion "Growth and order of automorphisms of free groups and free Burnside groups," Geometry & Topology, Geom. Topol. 21(4), 1969-2014, (2017)

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