Properties of the subsemigroups of the bicyclic monoid

L. Descalco, Nik Ruskuc

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
4 Downloads (Pure)


In this paper we study some properties of the subsemigroups of the bicyclic monoid B, by using a recent description of its subsemigroups. We start by giving necessary and sufficient conditions for a subsemigroup to be finitely generated. Then we show that all finitely generated subsemigroups are automatic and finitely presented. Finally we prove that a subsemigroup of B is residually finite if and only if it does not contain a copy of B.

Original languageEnglish
Pages (from-to)311-330
Number of pages20
JournalCzechoslovak Mathematical Journal
Issue number2
Publication statusPublished - Jun 2008


  • Bicyclic monoid
  • Subsemigroup
  • Generators
  • Defining relations
  • Automatic structures
  • Automatic semigroups


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