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On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations

Catarino, P and Higgins, PM and Levi, I (2015) 'On inverse subsemigroups of the semigroup of orientation-preserving or orientation-reversing transformations.' Algebra and Discrete Mathematics, 19 (2). 162 - 171. ISSN 1726-3255

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Abstract

It is well-known [16] that the semigroup Tn of all total transformations of a given n-element set Xn is covered by its inverse subsemigroups. This note provides a short and direct proof, based on properties of digraphs of transformations, that every inverse subsemigroup of order-preserving transformations on a finite chain Xn is a semilattice of idempotents, and so the semigroup of all order-preserving transformations of Xn is not covered by its inverse subsemigroups. This result is used to show that the semigroup of all orientation-preserving transformations and the semigroup of all orientation-preserving or orientation-reversing transformations of the chain Xn are covered by their inverse subsemigroups precisely when n≤3.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Jim Jamieson
Date Deposited: 05 Mar 2015 14:50
Last Modified: 08 Aug 2019 12:15
URI: http://repository.essex.ac.uk/id/eprint/13220

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