Publication
Primitive permutation groups and strongly factorizable transformation semigroups
| dc.contributor.author | Araújo, João | |
| dc.contributor.author | Bentz, Wolfram | |
| dc.contributor.author | Cameron, Peter | |
| dc.date.accessioned | 2023-01-30T16:11:56Z | |
| dc.date.available | 2023-01-30T16:11:56Z | |
| dc.date.issued | 2021-01-01 | |
| dc.description | Preprint de J. Araújo, W. Bentz, and P.J. Cameron, “Primitive Permutation Groups and Strongly Factorizable Transformation Semigroups”, Journal of Algebra 565 (2021), 513-530. | pt_PT |
| dc.description.abstract | Let Ω be a finite set and T (Ω) be the full transformation monoid on Ω. The rank of a transformation t ∈ T (Ω) is the natural number |Ωt|. Given A ⊆ T (Ω), denote by 〈A〉 the semigroup generated by A. Let k be a fixed natural number such that 2 ≤ k ≤ |Ω|. In the first part of this paper we (almost) classify the permutation groups G on Ω such that for all rank k transformations t ∈ T (Ω), every element in St := 〈G, t〉 can be written as a product eg, where e2 = e ∈ St and g ∈ G. In the second part we prove, among other results, that if S ≤ T (Ω) and G is the normalizer of S in the symmetric group on Ω, then the semigroup SG is regular if and only if S is regular. (Recall that a semigroup S is regular if for all s ∈ S there exists s′ ∈ S such that s = ss′s.) The paper ends with a list of problems. | pt_PT |
| dc.description.sponsorship | The first author was partially supported by the Funda ̧c ̃ao para a Ciˆencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the projects UIDB/00297/2020 (Centro de Matemtica e Aplicaes), PTDC/MAT-PUR/31174/2017, UIDB/04621/2020 and UIDP/04621/2020. | pt_PT |
| dc.description.version | info:eu-repo/semantics/publishedVersion | pt_PT |
| dc.identifier.citation | J. Araújo, W. Bentz, and P.J. Cameron, “Primitive Permutation Groups and Strongly Factorizable Transformation SemiGroups”, Journal of Algebra 565 (2021), 513-530. | pt_PT |
| dc.identifier.doi | 10.1016/j.jalgebra.2020.05.023 | pt_PT |
| dc.identifier.eissn | 1090-266X | |
| dc.identifier.issn | 0021-8693 | |
| dc.identifier.uri | http://hdl.handle.net/10400.2/13255 | |
| dc.language.iso | eng | pt_PT |
| dc.peerreviewed | yes | pt_PT |
| dc.publisher | Elsevier | pt_PT |
| dc.relation | Center for Mathematics and Applications | |
| dc.relation | Center for Computational and Stochastic Mathematics | |
| dc.relation | Center for Computational and Stochastic Mathematics | |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | pt_PT |
| dc.title | Primitive permutation groups and strongly factorizable transformation semigroups | pt_PT |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.awardTitle | Center for Mathematics and Applications | |
| oaire.awardTitle | Center for Computational and Stochastic Mathematics | |
| oaire.awardTitle | Center for Computational and Stochastic Mathematics | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F00297%2F2020/PT | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/3599-PPCDT/PTDC%2FMAT-PUR%2F31174%2F2017/PT | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDB%2F04621%2F2020/PT | |
| oaire.awardURI | info:eu-repo/grantAgreement/FCT/6817 - DCRRNI ID/UIDP%2F04621%2F2020/PT | |
| oaire.citation.endPage | 530 | pt_PT |
| oaire.citation.startPage | 513 | pt_PT |
| oaire.citation.title | Journal of Algebra | pt_PT |
| oaire.citation.volume | 565 | pt_PT |
| oaire.fundingStream | 6817 - DCRRNI ID | |
| oaire.fundingStream | 3599-PPCDT | |
| oaire.fundingStream | 6817 - DCRRNI ID | |
| oaire.fundingStream | 6817 - DCRRNI ID | |
| person.familyName | Ribeiro Soares Gonçalves de Araújo | |
| person.familyName | Bentz | |
| person.familyName | Cameron | |
| person.givenName | João Jorge | |
| person.givenName | Wolfram | |
| person.givenName | Peter | |
| person.identifier.ciencia-id | EC1F-273A-9F24 | |
| person.identifier.orcid | 0000-0001-6655-2172 | |
| person.identifier.orcid | 0000-0003-0002-1277 | |
| person.identifier.orcid | 0000-0003-3130-9505 | |
| person.identifier.scopus-author-id | 7202869893 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.identifier | http://doi.org/10.13039/501100001871 | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
| project.funder.name | Fundação para a Ciência e a Tecnologia | |
| rcaap.rights | openAccess | pt_PT |
| rcaap.type | article | pt_PT |
| relation.isAuthorOfPublication | 1f7b349c-3251-480d-a3ac-e3cb4ef44f22 | |
| relation.isAuthorOfPublication | 20420639-0e78-4226-a2e3-892cd2eaa7e8 | |
| relation.isAuthorOfPublication | 0bd89451-91f9-48d4-a05d-1175eca332fa | |
| relation.isAuthorOfPublication.latestForDiscovery | 1f7b349c-3251-480d-a3ac-e3cb4ef44f22 | |
| relation.isProjectOfPublication | cd254f72-96c1-4c38-9af6-3997cafdeea9 | |
| relation.isProjectOfPublication | 6c34e6c9-e6b8-40c2-b7c4-366d8cc84e13 | |
| relation.isProjectOfPublication | 3471b937-6390-4db2-873a-4c793b7d70ec | |
| relation.isProjectOfPublication | c7875204-9f77-467d-a299-dd1ffa14ff3b | |
| relation.isProjectOfPublication.latestForDiscovery | cd254f72-96c1-4c38-9af6-3997cafdeea9 |