Automaticity for graphs of groups

  • Susan Hermiller

    University of Nebraska, Lincoln, USA
  • Derek F. Holt

    University of Warwick, Coventry, UK
  • Tim Susse

    Bard College at Simon's Rock, Great Barrington, USA
  • Sarah Rees

    University of Newcastle, UK
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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.

Cite this article

Susan Hermiller, Derek F. Holt, Tim Susse, Sarah Rees, Automaticity for graphs of groups. Groups Geom. Dyn. 15 (2021), no. 2, pp. 503–551

DOI 10.4171/GGD/605