Bilateral semidirect product decompositions of transformation monoids

Author： Fernandes Vítor  

Publisher： Springer Publishing Company

ISSN： 0037-1912

Source： Semigroup Forum, Vol.82, Iss.2, 2011-04, pp. : 271-287

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Abstract

In this paper we consider the monoid $mathcal {OR}_{n}$ of all full transformations on a chain with n elements that preserve or reverse the orientation, as well as its submonoids $mathcal {OD}_{n}$ of all order-preserving or order-reversing elements, $mathcal {OP}_{n}$ of all orientation-preserving elements and $mathcal {O}_{n}$ of all order-preserving elements. By making use of some well known presentations, we show that each of these four monoids is a quotient of a bilateral semidirect product of two of its remarkable submonoids.

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