Maximal properties of some subsemigroups in finite order-preserving transformation semigroups
Xiuliang Yang, Lu Chunghan · Communications in Algebra · 2000
Let [n] = {1,2,…,n} be a finite set, ordered in the usual way. The order-preserving transformation semigroup On is the set of all order-preserving transformations of [n] (excluding the identity mapping) under composition. In this paper we first describe maximal idempotent-generated subsemigroups of O n, and show that On has 2n - 2 such subsemi-groups. Secondly, we investigate maximal regular subsemigroups of On , and obtain the number of such subsemigroups as 2n - 3. Thirdly, we describe maximal idempotent-generated regular subsemigroups of On , and also obtain their classification and number.