Geodesic
Automaticity for graphs of groups
Susan Hermiller1 ; Derek F. Holt2 ; Sarah Rees3 orcid ; Tim Susse4
1University of Nebraska, Lincoln, USA
2University of Warwick, Coventry, UK
3University of Newcastle, UK
4Bard College at Simon's Rock, Great Barrington, USA
Groups, geometry, and dynamics, Tome 15 (2021) no. 2, pp. 503-551

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DOI

In this article we construct asynchronous and sometimes synchronous automatic structures for amalgamated products and HNN extensions of groups that are strongly asynchronously (or synchronously) coset automatic with respect to the associated automatic subgroups, subject to further geometric conditions. These results are proved in the general context of fundamental groups of graphs of groups. The hypotheses of our closure results are satisfied in a variety of examples such as Artin groups of sufficiently large type, Coxeter groups, virtually abelian groups, and groups that are hyperbolic relative to virtually abelian subgroups.
DOI : 10.4171/ggd/605
Classification : 20-XX, 00-XX
Mots-clés : Automatic group, automatic coset system, graph of groups, relatively hyperbolic group, 3-manifold group, Artin group

Susan Hermiller  1   ; Derek F. Holt  2   ; Sarah Rees  3   ; Tim Susse  4

1 University of Nebraska, Lincoln, USA
2 University of Warwick, Coventry, UK
3 University of Newcastle, UK
4 Bard College at Simon's Rock, Great Barrington, USA 
Susan Hermiller; Derek F. Holt; Sarah Rees; Tim Susse. Automaticity for graphs of groups. Groups, geometry, and dynamics, Tome 15 (2021) no. 2, pp. 503-551. doi: 10.4171/ggd/605
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     author = {Susan Hermiller and Derek F. Holt and Sarah Rees and Tim Susse},
     title = {Automaticity for graphs of groups},
     journal = {Groups, geometry, and dynamics},
     pages = {503--551},
     year = {2021},
     volume = {15},
     number = {2},
     doi = {10.4171/ggd/605},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/605/}
}
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