Automatic groups associated with word orders other than shortlex


automatic groups, word orders


Published in Internat. J. Algebra Comput. 8 (1998), 575--598.


The existing algorithm to compute and verify the automata associated with an automatic group deals only with the subclass of shortlex automatic groups. This paper describes the extension of the algorithm to deal with automatic groups associated with other word orders (the algorithm has now been implemented) and reports on the use of the algorithm for specific examples; in particular a very natural automatic (or asynchonously automatic) structure for the Baumslag-Solitar and related classes of groups (closely related to one described for some of those groups by Epstein et al.) is found from a wreath product order over shortlex. \

The preprint is available as gzipped dvi (41 kB) and postscript (26 kB) files.

Alternatively, you can request a copy by e-mailing me.

Sarah Rees
11 July 1997