<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Fernandes, Vítor H.</style></author><author><style face="normal" font="default" size="100%">Quinteiro, Teresa M.</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">A note on bilateral semidirect product decompositions of some monoids of order-preserving partial permutations</style></title><secondary-title><style face="normal" font="default" size="100%">Bull. Korean Math. Soc.</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2016</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://pdf.medrang.co.kr/kms01/BKMS/53/BKMS-53-2-495-506.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">53</style></volume><pages><style face="normal" font="default" size="100%">495-506</style></pages><abstract><style face="normal" font="default" size="100%">&lt;p&gt;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 $\mathcal{C}_2$. &lt;/p&gt;
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