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Periodica Mathematica Hungarica

, Volume 75, Issue 2, pp 273–285 | Cite as

Infinite dual symmetric inverse monoids

  • James EastEmail author
Article
  • 75 Downloads

Abstract

Let \({\mathcal {I}}^*_X\) be the dual symmetric inverse monoid on an infinite set X. We show that \({\mathcal {I}}^*_X\) may be generated by the symmetric group \({\mathcal {S}}_X\) together with two (but no fewer) additional block bijections, and we classify the pairs \(\alpha ,\beta \in {\mathcal {I}}^*_X\) for which \({\mathcal {I}}^*_X\) is generated by \({\mathcal {S}}_X\,\cup \,\{\alpha ,\beta \}\). Among other results, we show that any countable subset of \({\mathcal {I}}^*_X\) is contained in a 4-generated subsemigroup of \({\mathcal {I}}^*_X\), and that the length function on \({\mathcal {I}}^*_X\) (and its finitary power semigroup) is bounded with respect to any generating set.

Keywords

Dual symmetric inverse monoids Symmetric groups Generators Idempotents Semigroup Bergman property Sierpiński rank 

Mathematics Subject Classification

20M20 20M18 

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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2017

Authors and Affiliations

  1. 1.Centre for Research in Mathematics, School of Computing, Engineering and MathematicsWestern Sydney UniversityPenrithAustralia

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