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Automatic semigroups and Bruck-Reilly extensions

A. J. CainContact Information

(1)  Centro de Matemático, Universidade do Porto, Rua do Campo Alegre 687, 4169-007 Porto, Portugal

Received: 17 March 2008  Revised: 16 June 2009  Accepted: 17 June 2009  Published online: 6 November 2009

Abstract  The interaction of automatic semigroups and Bruck-Reilly extensions is studied. It is proved that every automatic Bruck-Reilly extension has an automatic base semigroup. This result is then applied to answer negatively the question of Andrade et al. on whether automatic structures for Bruck-Reilly extensions of groups are characterized by the fellow traveller property. An example is exhibited to show that the class of automatic semigroups is not closed under forming Bruck-Reilly extensions.

Key words and phrases  automatic semigroup - Bruck-Reilly extension - fellow traveller property


2000 Mathematics Subject Classification  primary 20M05 - secondary 20M35, 68Q45


Contact Information A. J. Cain
Email: ajcain@fc.up.pt
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