Author(s): Fernandes, Vítor Hugo ; Quinteiro, Teresa
Date: 2016
Persistent ID: http://hdl.handle.net/10400.21/9710
Origin: Repositório Científico do Instituto Politécnico de Lisboa
Subject(s): Transformations; Partial isometries; Order-preserving; Semidirect products; Pseudovarieties; Transformations; Transformations; Partial isometries; Partial isometries; Order-preserving; Order-preserving; Semidirect products; Semidirect products; Pseudovarieties; Pseudovarieties
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 POIn and 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 C-2 of order two and, analogously, DPn is a quotient of a semidirect product of ODPn and C-2.
