A finite interval in the subsemigroup lattice of the full transformation monoid

J. Jonusas, J. D. Mitchell*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

In this paper we describe a portion of the subsemigroup lattice of the full transformation semigroup Omega (Omega) , which consists of all mappings on the countable infinite set Omega. Gavrilov showed that there are five maximal subsemigroups of Omega (Omega) containing the symmetric group . The portion of the subsemigroup lattice of Omega (Omega) which we describe is that between the intersection of these five maximal subsemigroups and Omega (Omega) . We prove that there are only 38 subsemigroups in this interval, in contrast to the subsemigroups between and Omega (Omega) .

Original languageEnglish
Pages (from-to)183-198
Number of pages16
JournalSemigroup Forum
Volume89
Issue number1
DOIs
Publication statusPublished - Aug 2014

Keywords

  • Transformation semigroups
  • Maximal subsemigroups
  • Lattice of subsemigroups
  • CLONES
  • SETS

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