Acta Mathematica Hungarica

, Volume 131, Issue 1, pp 1–24

Semitransitive subsemigroups of the singular part of the finite symmetric inverse semigroup

  • Karin Cvetko-Vah
  • Damjana Kokol Bukovšek
  • Tomaž Košir
  • Ganna Kudryavtseva
Article

DOI: 10.1007/s10474-011-0071-9

Cite this article as:
Cvetko-Vah, K., Kokol Bukovšek, D., Košir, T. et al. Acta Math Hung (2011) 131: 1. doi:10.1007/s10474-011-0071-9
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Abstract

We prove that the minimal cardinality of a semitransitive subsemigroup in the singular part \(\mathcal{I}_{n}\setminus \mathcal{S}_{n}\) of the symmetric inverse semigroup \(\mathcal{I}_{n}\) is 2np+1, where p is the greatest proper divisor of n, and classify all semitransitive subsemigroups of this minimal cardinality.

Key words and phrases

symmetric inverse semigroup singular part semitransitivity minimal cardinality 

2000 Mathematics Subject Classification

20M18 

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2011

Authors and Affiliations

  • Karin Cvetko-Vah
    • 1
  • Damjana Kokol Bukovšek
    • 1
  • Tomaž Košir
    • 1
  • Ganna Kudryavtseva
    • 2
  1. 1.Department of MathematicsUniversity of LjubljanaLjubljanaSlovenia
  2. 2.Centre for systems and information technologiesUniversity of Nova GoricaNova GoricaSlovenia

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