Automaton semigroup constructions

Tara Brough, Alan James Cain

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

The aim of this paper is to investigate whether the class of automaton semigroups is closed under certain semigroup constructions. We prove that the free product of two automaton semigroups that contain left identities is again an automaton semigroup. We also show that the class of automaton semigroups is closed under the combined operation of ‘free product followed by adjoining an identity’. We present an example of a free product of finite semigroups that we conjecture is not an automaton semigroup. Turning to wreath products, we consider two slight generalizations of the concept of an automaton semigroup, and show that a wreath product of an automaton monoid and a finite monoid arises as a generalized automaton semigroup in both senses. We also suggest a potential counterexample that would show that a wreath product of an automaton monoid and a finite monoid is not necessarily an automaton monoid in the usual sense.
Original languageEnglish
Pages (from-to)763-774
Number of pages12
JournalSemigroup Forum
Volume90
Issue number3
Early online date10 Oct 2014
DOIs
Publication statusPublished - 24 Dec 2014

Keywords

  • Automaton semigroup
  • Free product
  • Wreath product
  • Constructions

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