Automatic groups associated with word orders other than shortlex
Keywords automatic groups, word orders
Status 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.
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