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Automaticity for graphs of groups

Lookup NU author(s): Professor Sarah Rees

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This is the authors' accepted manuscript of an article that has been published in its final definitive form by European Mathematical Society Publishing House, 2021.

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Abstract

In this article we constructasynchronous and sometimes synchronous automaticstructures for amalgamated products and HNN extensionsof groups that arestrongly asynchronously (or synchronously) % SR added asynchronouslycoset automatic with respect to the associatedautomatic subgroups, subject to further geometric conditions.These results are proved in the general contextof fundamental groups of graphs of groups.The hypotheses of our closure resultsare satisfied in a variety of examples such asArtin groups of sufficiently large type, Coxeter groups, virtuallyabelian groups,and groups that are hyperbolic relative to virtuallyabelian subgroups.

Publication metadata

Author(s): Hermiller S, Holt D, Rees S, Susse T

Publication type: Article

Publication status: Published

Journal: Geometry, Groups and Dynamics

Year: 2021

Volume: 15

Issue: 2

Pages: 503–551

Print publication date: 06/08/2021

Online publication date: 01/04/2021

Acceptance date: 07/06/2020

Date deposited: 22/06/2020

ISSN (print): 1661-7207

ISSN (electronic): 1661-7215

Publisher: European Mathematical Society Publishing House

URL: https://doi.org/10.4171/GGD/605

DOI: 10.4171/GGD/605

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