Semitransitive subsemigroups of the singular part of the finite symmetric inverse semigroup

Abstract

We prove that the minimal cardinality of the semitransitive subsemigroup in the singular part $\IS_n\setminus §_n$ of the symmetric inverse semigroup $\IS_n$ is $2n-p+1$, where $p$ is the greatest proper divisor of $n$, and classify all semitransitive subsemigroups of this minimal cardinality.

References in corpus (2)

• Strictly semi-transitive operator algebras
• Semitransitive and transitive subsemigroups of the inverse symmetric semigroups

Cited by in corpus (1)

• On a stronger reconstruction notion for monoids and clones