## Abstract

In this note we consider the monoid PODI_{n} of all monotone partial permutations on {1,..., n} and its submonoids DP_{n}, POI_{n} and ODP_{n} of all partial isometries, of all order-preserving partial permutations and of all order-preserving partial isometries, respectively. We prove that both the monoids POI_{n}and ODP_{n} are quotients of bilateral semidirect products of two of their remarkable submonoids, namely of extensive and of co-extensive transformations. Moreover, we show that PODI_{n} is a quotient of a semidirect product of POI_{n} and the group C_{2} of order two and, analogously, DP_{n} is a quotient of a semidirect product of ODP_{n} and C_{2}.

Original language | English |
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Pages (from-to) | 495-506 |

Number of pages | 12 |

Journal | Bulletin of the Korean Mathematical Society |

Volume | 53 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2016 |

## Keywords

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