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Centralisers of linear growth automorphisms of free groups
Published online by Cambridge University Press: 20 September 2024
Abstract
In this note we investigate the centraliser of a linearly growing element of $\mathrm{Out}(F_n)$ (that is, a root of a Dehn twist automorphism), and show that it has a finite index subgroup mapping onto a direct product of certain “equivariant McCool groups” with kernel a finitely generated free abelian group. In particular, this allows us to show it is VF and hence finitely presented.
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- Research Article
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- © The Author(s), 2024. Published by Cambridge University Press on behalf of Cambridge Philosophical Society