On the monoid of all injective orientation-preserving and extensive partial transformations

Let POP epsilon I-n be the monoid of all injective orientation-preserving and extensive partial transformations on {1, 2, ..., n} ordered in the standard way. In this paper, we determine the minimum generating set and the minimum quasi-idempotent generating set of POP epsilon I-n, and so the rank and the quasi-idempotent rank of POP epsilon I-n are obtained. Moreover, we describe the maximal subsemigroups and maximal quasi-idempotent generated subsemigroups of POP epsilon I-n and completely obtain their classifications.