Automatic semigroups and Bruck–Reilly extensions
نویسنده
چکیده
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.
منابع مشابه
Automatic structures for semigroup constructions
We survey results concerning automatic structures for semigroup constructions, providing references and describing the corresponding automatic structures. The constructions we consider are: free products, direct products, Rees matrix semigroups, Bruck-Reilly extensions and wreath products.
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