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
|
Text
Semigroup Forum Involution paper 2019.pdf - Accepted Version Download (229kB) | Preview |
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 |
Actions (login required)
 |
View Item |
Altmetric
Altmetric