ON THE MAXIMAL SUBSEMIGROUPS OF SOME TRANSFORMATION SEMIGROUPS

Let Singn be the semigroup of all singular transformations on an n-element set. We consider two subsemigroups of Singn: the semigroup On of all isotone singular transformations and the semigroup Mn of all monotone singular transformations. We describe the maximal subsemigroups of these two semigroups, and study the connections between them.