|Automatic semigroups and Bruck–Reilly extensions
Cain, Alan J.
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.