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Zbl 1108.20056
Cain, Alan J.
A group-embeddable non-automatic semigroup whose universal group is automatic. (English)
[J] Glasg. Math. J. 48, No. 2, 337-342 (2006). ISSN 0017-0895; ISSN 1469-509X

The author gives a counter example for the following problem raised by M.~Hoffman (2000) and M.~E.~Kambites (2003) in their Ph.D. theses. It is shown that there exists a finitely generated semigroup $S$ that is embeddable in a group such that the universal group of $S$ is automatic, but $S$ is not automatic. At the end of the paper, the author states a modified problem: whether $S$ is required to be finitely presented.
[Tero J. Harju (Turku)]

MSC 2000:: *20M05 Free semigroups
20M35 Semigroups in automata theory, linguistics, etc.

Keywords: automatic semigroups; automatic groups; universal groups; group-embeddable semigroups; finitely generated semigroups

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