Semitransitive and transitive subsemigroups of the inverse symmetric semigroups

TL;DR

This paper classifies minimal transitive and semitransitive subsemigroups within inverse symmetric semigroups, linking their properties to the classification of transitive subgroups in finite symmetric groups.

Contribution

It provides a classification of minimal transitive and semitransitive subsemigroups of inverse symmetric semigroups, extending the understanding of their structure relative to symmetric groups.

Findings

Classification of minimal transitive subsemigroups achieved

Classification of minimal semitransitive subsemigroups achieved

Results relate subsemigroup properties to subgroup classifications in symmetric groups

Abstract

We classify minimal transitive subsemigroups of the finitary inverse symmetric semigroup modulo the classification of minimal transitive subgroups of finite symmetric groups; and semitransitive subsemigroups of the finite inverse symmetric semigroup of the minimal cardinality modulo the classification of transitive subgroups of the minimal cardinality of finite symmetric groups.