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Primitive permutation groups and strongly factorizable transformation semigroups
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dc.contributor.author | Araújo, João | |
dc.contributor.author | Bentz, Wolfram | |
dc.contributor.author | Cameron, Peter J. | |
dc.date.accessioned | 2021-05-31T23:41:04Z | |
dc.date.available | 2021-05-31T23:41:04Z | |
dc.date.issued | 2021-01-01 | |
dc.identifier | 268229031 | |
dc.identifier | 73ec734e-b8cf-4139-b9cc-347df72d88f0 | |
dc.identifier | 85085933520 | |
dc.identifier | 000581500500018 | |
dc.identifier.citation | Araújo , J , Bentz , W & Cameron , P J 2021 , ' Primitive permutation groups and strongly factorizable transformation semigroups ' , Journal of Algebra , vol. 565 , pp. 513-530 . https://doi.org/10.1016/j.jalgebra.2020.05.023 | en |
dc.identifier.issn | 0021-8693 | |
dc.identifier.other | ORCID: /0000-0003-3130-9505/work/75248643 | |
dc.identifier.uri | https://hdl.handle.net/10023/23289 | |
dc.description | Funding: The first author was partially supported by the Fundação para a Ciênciae 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. | en |
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 in T(Ω) is the natural number |Ωt|. Given a subset A of 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 in T(Ω), every element in St = ⟨G,t⟩ can be written as a product eg, where e is an idempotent in 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 x∈S there exists y∈S such that x = xyx.) The paper ends with a list of problems. | |
dc.format.extent | 276164 | |
dc.language.iso | eng | |
dc.relation.ispartof | Journal of Algebra | en |
dc.subject | Primitive groups | en |
dc.subject | Transformation semigroups | en |
dc.subject | Factorizable semigroups | en |
dc.subject | Regular semigroups | en |
dc.subject | QA Mathematics | en |
dc.subject | Mathematics(all) | en |
dc.subject | T-NDAS | en |
dc.subject.lcc | QA | en |
dc.title | Primitive permutation groups and strongly factorizable transformation semigroups | en |
dc.type | Journal article | en |
dc.contributor.institution | University of St Andrews. Pure Mathematics | en |
dc.contributor.institution | University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra | en |
dc.identifier.doi | 10.1016/j.jalgebra.2020.05.023 | |
dc.description.status | Peer reviewed | en |
dc.date.embargoedUntil | 2021-06-01 |
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