RESEARCH ARTICLE

Classification of $\mathscr{L}$-cross-sections of the finite symmetric semigroup up to isomorphism

Eugenija Bondar<sup>ab

a</sup> Luhansk Taras Shevchenko National University
^b Ural Federal University

Abstract: Let $\mathscr{T}_n$ be the symmetric semigroup of full transformations on a finite set with $n$ elements. In the paper we give a counting formula for the number of $\mathscr{L}$-cross-sections of $\mathscr{T}_n$ and classify all $\mathscr{L}$-cross-sections of $\mathscr{T}_n$ up to isomorphism.

Keywords: symmetric semigroup, cross-section, Green's relations.

MSC: 20M20

Received: 04.06.2014
Revised: 08.10.2015

Language: English

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