Identidades polinomiais via identidades de grupo : a conjectura de Brian Hartley

Detalhes bibliográficos
Autor(a) principal: Silva, Dalton Couto
Data de Publicação: 2017
Tipo de documento: Dissertação
Idioma: por
Título da fonte: Repositório Institucional da UFSCAR
Texto Completo: https://repositorio.ufscar.br/handle/ufscar/9356
Resumo: In this work, we present the Conjecture of Brian Hartley and study its validity, i.e, we verify if group identities in the unity group U(FG) make FG satisfy a polynomial identity, where G is a torsion group and F any field. This study will be made first for infinite fields, and next for any field. From this result, will be deduced necessary and suficient conditions in a group G, for the unity group U(FG) satisfy group identities.
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spelling Silva, Dalton CoutoTalpo, Humberto Luizhttp://lattes.cnpq.br/1674689444257254http://lattes.cnpq.br/4403658004588089df535c2a-3ef6-4f36-aa93-58c9649f6c1c2018-01-31T18:58:00Z2018-01-31T18:58:00Z2017-02-16SILVA, Dalton Couto. Identidades polinomiais via identidades de grupo : a conjectura de Brian Hartley. 2017. Dissertação (Mestrado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2017. Disponível em: https://repositorio.ufscar.br/handle/ufscar/9356.https://repositorio.ufscar.br/handle/ufscar/9356In this work, we present the Conjecture of Brian Hartley and study its validity, i.e, we verify if group identities in the unity group U(FG) make FG satisfy a polynomial identity, where G is a torsion group and F any field. This study will be made first for infinite fields, and next for any field. From this result, will be deduced necessary and suficient conditions in a group G, for the unity group U(FG) satisfy group identities.Neste trabalho, apresentamos a Conjectura de Brian Hartley e estudamos sua validade, ou seja, verificamos se identidades de grupo no grupo das unidades U(FG) levam FG a satisfazer identidades polinomiais, onde G e um grupo de torçao e F corpo qualquer. Tal estudo sera realizado primeiramente para corpos infinitos, e em seguida para corpos quaisquer. A partir deste resultado, serao deduzidas condicoes necessarias e suficientes em um grupo G, para que o grupo das unidades U(FG) satisfaca identidades de grupo.Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)porUniversidade Federal de São CarlosCâmpus São CarlosPrograma de Pós-Graduação em Matemática - PPGMUFSCarConjectura de Brian HartleyIdentidades polinomiaisConjecture of Brian HartleyPolynomial identityCIENCIAS EXATAS E DA TERRA::MATEMATICAIdentidades polinomiais via identidades de grupo : a conjectura de Brian Hartleyinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/masterThesisOnline600600d36b9ec5-6583-4a3a-a534-73d7ad1b9a2einfo:eu-repo/semantics/openAccessreponame:Repositório Institucional da UFSCARinstname:Universidade Federal de São Carlos (UFSCAR)instacron:UFSCARORIGINALDissDCS.pdfDissDCS.pdfapplication/pdf770561https://repositorio.ufscar.br/bitstream/ufscar/9356/1/DissDCS.pdfbe9bc14e68967a56c035cb7a1a5557a4MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81957https://repositorio.ufscar.br/bitstream/ufscar/9356/2/license.txtae0398b6f8b235e40ad82cba6c50031dMD52TEXTDissDCS.pdf.txtDissDCS.pdf.txtExtracted texttext/plain149872https://repositorio.ufscar.br/bitstream/ufscar/9356/3/DissDCS.pdf.txt292e2c22bf810f5a57fb190c652b0d6cMD53THUMBNAILDissDCS.pdf.jpgDissDCS.pdf.jpgIM Thumbnailimage/jpeg6718https://repositorio.ufscar.br/bitstream/ufscar/9356/4/DissDCS.pdf.jpg8e797516b3ca833cade3f4790bbc8dd8MD54ufscar/93562023-09-18 18:31:12.009oai:repositorio.ufscar.br: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Repositório InstitucionalPUBhttps://repositorio.ufscar.br/oai/requestopendoar:43222023-09-18T18:31:12Repositório Institucional da UFSCAR - Universidade Federal de São Carlos (UFSCAR)false
dc.title.por.fl_str_mv Identidades polinomiais via identidades de grupo : a conjectura de Brian Hartley
title Identidades polinomiais via identidades de grupo : a conjectura de Brian Hartley
spellingShingle Identidades polinomiais via identidades de grupo : a conjectura de Brian Hartley
Silva, Dalton Couto
Conjectura de Brian Hartley
Identidades polinomiais
Conjecture of Brian Hartley
Polynomial identity
CIENCIAS EXATAS E DA TERRA::MATEMATICA
title_short Identidades polinomiais via identidades de grupo : a conjectura de Brian Hartley
title_full Identidades polinomiais via identidades de grupo : a conjectura de Brian Hartley
title_fullStr Identidades polinomiais via identidades de grupo : a conjectura de Brian Hartley
title_full_unstemmed Identidades polinomiais via identidades de grupo : a conjectura de Brian Hartley
title_sort Identidades polinomiais via identidades de grupo : a conjectura de Brian Hartley
author Silva, Dalton Couto
author_facet Silva, Dalton Couto
author_role author
dc.contributor.authorlattes.por.fl_str_mv http://lattes.cnpq.br/4403658004588089
dc.contributor.author.fl_str_mv Silva, Dalton Couto
dc.contributor.advisor1.fl_str_mv Talpo, Humberto Luiz
dc.contributor.advisor1Lattes.fl_str_mv http://lattes.cnpq.br/1674689444257254
dc.contributor.authorID.fl_str_mv df535c2a-3ef6-4f36-aa93-58c9649f6c1c
contributor_str_mv Talpo, Humberto Luiz
dc.subject.por.fl_str_mv Conjectura de Brian Hartley
Identidades polinomiais
topic Conjectura de Brian Hartley
Identidades polinomiais
Conjecture of Brian Hartley
Polynomial identity
CIENCIAS EXATAS E DA TERRA::MATEMATICA
dc.subject.eng.fl_str_mv Conjecture of Brian Hartley
Polynomial identity
dc.subject.cnpq.fl_str_mv CIENCIAS EXATAS E DA TERRA::MATEMATICA
description In this work, we present the Conjecture of Brian Hartley and study its validity, i.e, we verify if group identities in the unity group U(FG) make FG satisfy a polynomial identity, where G is a torsion group and F any field. This study will be made first for infinite fields, and next for any field. From this result, will be deduced necessary and suficient conditions in a group G, for the unity group U(FG) satisfy group identities.
publishDate 2017
dc.date.issued.fl_str_mv 2017-02-16
dc.date.accessioned.fl_str_mv 2018-01-31T18:58:00Z
dc.date.available.fl_str_mv 2018-01-31T18:58:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/masterThesis
format masterThesis
status_str publishedVersion
dc.identifier.citation.fl_str_mv SILVA, Dalton Couto. Identidades polinomiais via identidades de grupo : a conjectura de Brian Hartley. 2017. Dissertação (Mestrado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2017. Disponível em: https://repositorio.ufscar.br/handle/ufscar/9356.
dc.identifier.uri.fl_str_mv https://repositorio.ufscar.br/handle/ufscar/9356
identifier_str_mv SILVA, Dalton Couto. Identidades polinomiais via identidades de grupo : a conjectura de Brian Hartley. 2017. Dissertação (Mestrado em Matemática) – Universidade Federal de São Carlos, São Carlos, 2017. Disponível em: https://repositorio.ufscar.br/handle/ufscar/9356.
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dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
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dc.publisher.none.fl_str_mv Universidade Federal de São Carlos
Câmpus São Carlos
dc.publisher.program.fl_str_mv Programa de Pós-Graduação em Matemática - PPGM
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publisher.none.fl_str_mv Universidade Federal de São Carlos
Câmpus São Carlos
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