Primitive permutation groups and strongly factorizable transformation semigroups

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MetadadosDescriçãoIdioma
Autor(es): dc.creatorAraújo, João-
Autor(es): dc.creatorBentz, Wolfram-
Autor(es): dc.creatorCameron, Peter-
Data de aceite: dc.date.accessioned2025-08-21T15:11:51Z-
Data de disponibilização: dc.date.available2025-08-21T15:11:51Z-
Data de envio: dc.date.issued2023-01-29-
Data de envio: dc.date.issued2023-01-29-
Data de envio: dc.date.issued2020-12-31-
Fonte completa do material: dc.identifierhttp://hdl.handle.net/10400.2/13255-
Fonte: dc.identifier.urihttp://educapes.capes.gov.br/handle/10400.2/13255-
Descrição: dc.descriptionPreprint de J. Araújo, W. Bentz, and P.J. Cameron, “Primitive Permutation Groups and Strongly Factorizable Transformation Semigroups”, Journal of Algebra 565 (2021), 513-530.-
Descrição: dc.descriptionLet 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.-
Descrição: dc.descriptionThe 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.-
Descrição: dc.descriptioninfo:eu-repo/semantics/publishedVersion-
Formato: dc.formatapplication/pdf-
Idioma: dc.languageen-
Publicador: dc.publisherElsevier-
Relação: dc.relationCenter for Mathematics and Applications-
Relação: dc.relationCenter for Computational and Stochastic Mathematics-
Relação: dc.relationCenter for Computational and Stochastic Mathematics-
Direitos: dc.rightshttp://creativecommons.org/licenses/by/4.0/-
Título: dc.titlePrimitive permutation groups and strongly factorizable transformation semigroups-
Aparece nas coleções:Repositório Aberto - Universidade Aberta (Portugal)

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