Automaticity for graphs of groups
Susan Hermiller, Derek F. Holt, Sarah Rees and Tim Susse
Keywords
Automatic groups, automatic coset system, graph of groups,
relatively hyperbolic group, 3-manifold group, Artin group
Status
Published in Geometry, Groups and Dynamics 15 (2021) 503--551
Abstract
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.
The preprint is available as a gzipped
pdf file.
Alternatively, you can request a copy by
e-mailing me.