Geometry & Topology

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

Rémi Coulon and Arnaud Hilion

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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.

Article information

Geom. Topol., Volume 21, Number 4 (2017), 1969-2014.

Received: 15 October 2013
Revised: 10 May 2016
Accepted: 6 September 2016
First available in Project Euclid: 19 October 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20E05: Free nonabelian groups 20E36: Automorphisms of infinite groups [For automorphisms of finite groups, see 20D45] 20F28: Automorphism groups of groups [See also 20E36] 20F50: Periodic groups; locally finite groups 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx]
Secondary: 68R15: Combinatorics on words

automorphism groups free groups Burnside groups growth of automorphisms train-track theory


Coulon, Rémi; Hilion, Arnaud. Growth and order of automorphisms of free groups and free Burnside groups. Geom. Topol. 21 (2017), no. 4, 1969--2014. doi:10.2140/gt.2017.21.1969.

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