The monoid of all orientation-preserving and extensive full transformations on a finite chain

Abstract

Let [Formula: see text] be the monoid of all orientation-preserving and extensive full transformations on [Formula: see text] ordered in the standard way. In this paper, we determine the minimum generating set and the minimum idempotent generating set of [Formula: see text], and so the rank and the idempotent rank of [Formula: see text] are obtained. Moreover, we describe maximal subsemigroups and maximal idempotent generated subsemigroups of [Formula: see text] and completely obtain their classifications.