The Geometry of Automatic Monoids
by
Pedro V. Silva
University of Porto, Porto, Portugal
Coauthors: Benjamin Steinberg (University of Porto)

It is well-known that automatic groups can be characterized using geometric properties of their Cayley graphs. Along the same line of thought, we provide a geometric characterization of automatic monoids. This involves working with a slightly strengthened definition of an automatic monoid (called p-automatic) which is still a proper generalization of the concept of an automatic group. The two definitions coincide in the case of right cancellative monoids for which a particularly simple characterization is obtained. Various results on submonoids and extensions of automatic and p-automatic monoids are also obtained. We give particular attention to rational submonoids of (p-)automatic monoids, being able to show in many cases that (p-)automaticity is inherited, with the sharpest results concerning rational subgroups. Also, closure properties are established for various notions of extensions of (p-)automatic monoids, including different types of products, ideal extensions, and Rees matrix constructions.

Date received: March 13, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caec-05.