A note on bilateral semidirect product decompositions of some monoids of order-preserving partial permutations

Vítor H. Fernandes, Teresa M. Quinteiro

Research output: Contribution to journalArticle

Abstract

In this note we consider the monoid PODIn of all monotone partial permutations on {1,..., n} and its submonoids DPn, POIn and ODPn of all partial isometries, of all order-preserving partial permutations and of all order-preserving partial isometries, respectively. We prove that both the monoids POInand ODPn are quotients of bilateral semidirect products of two of their remarkable submonoids, namely of extensive and of co-extensive transformations. Moreover, we show that PODIn is a quotient of a semidirect product of POIn and the group C2 of order two and, analogously, DPn is a quotient of a semidirect product of ODPn and C2.

Original languageEnglish
Pages (from-to)495-506
Number of pages12
JournalBulletin of the Korean Mathematical Society
Volume53
Issue number2
DOIs
Publication statusPublished - 2016

Keywords

  • Transformations
  • P*artial isometries
  • Order-preserving
  • Semidirect products
  • Pseudovarieties

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