Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

HOME ALL ARTICLES View

Bull. Korean Math. Soc. 2016; 53(2): 495-506

Printed March 31, 2016

https://doi.org/10.4134/BKMS.2016.53.2.495

Copyright © The Korean Mathematical Society.

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

V\'\i tor H. Fernandes and Teresa M. Quinteiro

Universidade NOVA de Lisboa, Instituto Superior de Engenharia de Lisboa

Abstract

In this note we consider the monoid $\PODI_n$ of all monotone partial permutations on $\{1,\ldots,n\}$ 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 $\mathcal{C}_2$ of order two and, analogously, $\DP_n$ is a quotient of a semidirect product of $\ODP_n$ and $\mathcal{C}_2$.

Keywords: transformations, partial isometries, order-preserving, semidirect products, pseudovarieties

MSC numbers: 20M20, 20M07, 20M10, 20M35

Stats or Metrics

Share this article on :

Related articles in BKMS

more +