Primitive permutation groups and strongly factorizable transformation semigroups

Detalhes bibliográficos
Autor(a) principal: Araújo, João
Data de Publicação: 2021
Outros Autores: Bentz, Wolfram, Cameron, Peter
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.2/13255
Resumo: 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.
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spelling Primitive permutation groups and strongly factorizable transformation semigroupsPreprint de J. Araújo, W. Bentz, and P.J. Cameron, “Primitive Permutation Groups and Strongly Factorizable Transformation Semigroups”, Journal of Algebra 565 (2021), 513-530.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.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.ElsevierRepositório AbertoAraújo, JoãoBentz, WolframCameron, Peter2023-01-30T16:11:56Z2021-01-012021-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/13255engJ. Araújo, W. Bentz, and P.J. Cameron, “Primitive Permutation Groups and Strongly Factorizable Transformation SemiGroups”, Journal of Algebra 565 (2021), 513-530.0021-869310.1016/j.jalgebra.2020.05.0231090-266Xinfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-16T15:44:46Zoai:repositorioaberto.uab.pt:10400.2/13255Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:52:17.418648Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Primitive permutation groups and strongly factorizable transformation semigroups
title Primitive permutation groups and strongly factorizable transformation semigroups
spellingShingle Primitive permutation groups and strongly factorizable transformation semigroups
Araújo, João
title_short Primitive permutation groups and strongly factorizable transformation semigroups
title_full Primitive permutation groups and strongly factorizable transformation semigroups
title_fullStr Primitive permutation groups and strongly factorizable transformation semigroups
title_full_unstemmed Primitive permutation groups and strongly factorizable transformation semigroups
title_sort Primitive permutation groups and strongly factorizable transformation semigroups
author Araújo, João
author_facet Araújo, João
Bentz, Wolfram
Cameron, Peter
author_role author
author2 Bentz, Wolfram
Cameron, Peter
author2_role author
author
dc.contributor.none.fl_str_mv Repositório Aberto
dc.contributor.author.fl_str_mv Araújo, João
Bentz, Wolfram
Cameron, Peter
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.
publishDate 2021
dc.date.none.fl_str_mv 2021-01-01
2021-01-01T00:00:00Z
2023-01-30T16:11:56Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.2/13255
url http://hdl.handle.net/10400.2/13255
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv J. Araújo, W. Bentz, and P.J. Cameron, “Primitive Permutation Groups and Strongly Factorizable Transformation SemiGroups”, Journal of Algebra 565 (2021), 513-530.
0021-8693
10.1016/j.jalgebra.2020.05.023
1090-266X
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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