Higgins, Peter M (2014) Permutations of a semigroup that map to inverses. Semigroup Forum, 89 (1). pp. 169-182. DOI https://doi.org/10.1007/s00233-013-9535-2
Higgins, Peter M (2014) Permutations of a semigroup that map to inverses. Semigroup Forum, 89 (1). pp. 169-182. DOI https://doi.org/10.1007/s00233-013-9535-2
Higgins, Peter M (2014) Permutations of a semigroup that map to inverses. Semigroup Forum, 89 (1). pp. 169-182. DOI https://doi.org/10.1007/s00233-013-9535-2
Abstract
We investigate the question as to when the members of a finite regular semigroup may be permuted in such a way that each member is mapped to one of its inverses. In general this is not possible. However we reformulate the problem in terms of a related graph and, using an application of Hall’s Marriage Lemma, we show in particular that the finite full transformation semigroup does enjoy this property.
| Item Type: | Article |
|---|---|
| Additional Information: | 14 pages |
| Uncontrolled Keywords: | Permutation matching; Hall's Marriage lemma; Full transformation semigroup; Finite regular semigroup |
| 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: | 12 Nov 2014 14:10 |
| Last Modified: | 18 Aug 2022 11:06 |
| URI: | http://repository.essex.ac.uk/id/eprint/11534 |
Available files
Filename: Permutations by inverses final.pdf