, Volume 131, Issue 1-2, pp 1-24
Date: 25 Feb 2011

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

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We prove that the minimal cardinality of a semitransitive subsemigroup in the singular part \(\mathcal{I}_{n}\setminus \mathcal{S}_{n}\) of the symmetric inverse semigroup \(\mathcal{I}_{n}\) is 2np+1, where p is the greatest proper divisor of n, and classify all semitransitive subsemigroups of this minimal cardinality.

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