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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.

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Acta Mathematica Hungarica
Authors: C. Campbell, E. Robertson, M. Ruškuc, and R. Thomas
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