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 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