A remark on divisibility of definable groups

Detalhes bibliográficos
Autor(a) principal: Edmundo, Mário Jorge
Data de Publicação: 2005
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.2/2842
Resumo: We show that if G is a definably compact, definably connected definable group defined in an arbitrary o-minimal structure, then G is divisible. Furthermore, if G is defined in an o-minimal expansion of a field, k ∈ ℕ and p_k: G → G is the definable map given by p_k(x) = x^k for all x ∈ G, then we have |(p_k)^{-1}(x)| ≥ k^r for all x ∈ G, where r > 0 is the maximal dimension of abelian definable subgroups of G.
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spelling A remark on divisibility of definable groupsDefinable groupsO-minimal structuresWe show that if G is a definably compact, definably connected definable group defined in an arbitrary o-minimal structure, then G is divisible. Furthermore, if G is defined in an o-minimal expansion of a field, k ∈ ℕ and p_k: G → G is the definable map given by p_k(x) = x^k for all x ∈ G, then we have |(p_k)^{-1}(x)| ≥ k^r for all x ∈ G, where r > 0 is the maximal dimension of abelian definable subgroups of G.WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimRepositório AbertoEdmundo, Mário Jorge2014-01-21T21:22:38Z2005-112005-11-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.2/2842engEdmundo, Mário Jorge - A remark on divisibility of definable groups. "Mathematical Logic Quarterly" [Em linha]. ISSN 0942-5616 (Print) 1521-3870 (Online).Vol. 51, Nº 6 (2005), p. 1-71521-3870info: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:RCAAP2023-11-16T15:16:42Zoai:repositorioaberto.uab.pt:10400.2/2842Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T22:44:09.143174Repositório 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 A remark on divisibility of definable groups
title A remark on divisibility of definable groups
spellingShingle A remark on divisibility of definable groups
Edmundo, Mário Jorge
Definable groups
O-minimal structures
title_short A remark on divisibility of definable groups
title_full A remark on divisibility of definable groups
title_fullStr A remark on divisibility of definable groups
title_full_unstemmed A remark on divisibility of definable groups
title_sort A remark on divisibility of definable groups
author Edmundo, Mário Jorge
author_facet Edmundo, Mário Jorge
author_role author
dc.contributor.none.fl_str_mv Repositório Aberto
dc.contributor.author.fl_str_mv Edmundo, Mário Jorge
dc.subject.por.fl_str_mv Definable groups
O-minimal structures
topic Definable groups
O-minimal structures
description We show that if G is a definably compact, definably connected definable group defined in an arbitrary o-minimal structure, then G is divisible. Furthermore, if G is defined in an o-minimal expansion of a field, k ∈ ℕ and p_k: G → G is the definable map given by p_k(x) = x^k for all x ∈ G, then we have |(p_k)^{-1}(x)| ≥ k^r for all x ∈ G, where r > 0 is the maximal dimension of abelian definable subgroups of G.
publishDate 2005
dc.date.none.fl_str_mv 2005-11
2005-11-01T00:00:00Z
2014-01-21T21:22:38Z
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/10400.2/2842
url http://hdl.handle.net/10400.2/2842
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Edmundo, Mário Jorge - A remark on divisibility of definable groups. "Mathematical Logic Quarterly" [Em linha]. ISSN 0942-5616 (Print) 1521-3870 (Online).Vol. 51, Nº 6 (2005), p. 1-7
1521-3870
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 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
publisher.none.fl_str_mv WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
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
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
repository.mail.fl_str_mv
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