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

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

2009-02-09

arxiv.org/abs/0902.1470v1

Mathematics

Group Theory

Scientific paper

We prove that the minimal cardinality of the semitransitive subsemigroup in
the singular part $\IS_n\setminus \S_n$ 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.

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