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).
pp. 162-171.

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).
pp. 162-171.

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).
pp. 162-171.

## 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 |
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Subjects: | Q Science > QA Mathematics |

Divisions: | Faculty of Science and Health Faculty of Science and Health > Mathematical Sciences, Department of |

SWORD Depositor: | Unnamed user with email elements@essex.ac.uk |

Depositing User: | Unnamed user with email elements@essex.ac.uk |

Date Deposited: | 05 Mar 2015 14:50 |

Last Modified: | 15 Jan 2022 00:45 |

URI: | http://repository.essex.ac.uk/id/eprint/13220 |

## Available files

**Filename:** document.pdf