Maximal properties of some subsemigroups in finite order-preserving transformation semigroups

Abstract

Let [n] = {1,2,…,n} be a finite set, ordered in the usual way. The order-preserving transformation semigroup O_n 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 O_n has 2n - 2 such subsemi-groups. Secondly, we investigate maximal regular subsemigroups of O_n , and obtain the number of such subsemigroups as 2n - 3. Thirdly, we describe maximal idempotent-generated regular subsemigroups of O_n , and also obtain their classification and number.

Keywords:

• finite rransformation semigroup
• order-preserving rransformation
• maximal idempotent-generated subsemigroup
• maximal regular subsemigroup
• maximal idempotent-generated regular subsemigroup

AMS 1991 subject classification:

• 20M20

¹This work is supported by N. S. F. of Guizhou Province

¹This work is supported by N. S. F. of Guizhou Province

Notes

¹This work is supported by N. S. F. of Guizhou Province