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Involution matchings, the semigroup of orientation-preserving and orientation-reversing mappings, and inverse covers of the full transformation semigroup

Higgins, Peter M (2019) 'Involution matchings, the semigroup of orientation-preserving and orientation-reversing mappings, and inverse covers of the full transformation semigroup.' Semigroup Forum, 98 (3). 669 - 689. ISSN 0037-1912

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Abstract

We continue the study of permutations of a fi nite regular semigroup that map each element to one of its inverses, providing a complete description in the case of semigroups whose idempotent generated subsemigroup is a union of groups. We show, in two ways, how to construct an involution matching on the semigroup of all transformations which either preserve or reverse orientation of a cycle. Finally, as an application, we use involution matchings to prove that when the base set has at least four members, a fi nite full transformation semigroup has no cover by inverse subsemigroups that is closed under intersection.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Elements
Date Deposited: 01 Apr 2019 15:48
Last Modified: 29 Mar 2020 01:00
URI: http://repository.essex.ac.uk/id/eprint/24377

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