An Arad and Fisman&apos

[EN] A theorem of Z. Arad and E. Fisman establishes that if A and B are two non-trivial conjugacy classes of a finite group G such that either AB = A boolean OR B or AB = A(-1) boolean OR B, then G cannot be a non-abelian simple group. We demonstrate that, in fact, < A > = < B &...

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Autores: Beltrán Felip, Antonio, Melchor, Carmen, Felipe Román, María Josefa|||0000-0002-6699-3135
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/194638
Acceso en línea:https://riunet.upv.es/handle/10251/194638
Access Level:acceso abierto
Palabra clave:Conjugacy classes
Products of conjugacy classes
Solvability criterium
MATEMATICA APLICADA
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spelling An Arad and Fisman&aposs theorem on products of conjugacy classes revisitedBeltrán Felip, AntonioMelchor, CarmenFelipe Román, María Josefa|||0000-0002-6699-3135Conjugacy classesProducts of conjugacy classesSolvability criteriumMATEMATICA APLICADA[EN] A theorem of Z. Arad and E. Fisman establishes that if A and B are two non-trivial conjugacy classes of a finite group G such that either AB = A boolean OR B or AB = A(-1) boolean OR B, then G cannot be a non-abelian simple group. We demonstrate that, in fact, < A > = < B > is solvable, the elements of A and B are p-elements for some prime p, and < A > is p-nilpotent. Moreover, under the second assumption, it turns out that A = B. This research is done by appealing to recently developed techniques and results that are based on the Classification of Finite Simple Groups.The authors thank the referee for careful reading that helped to improve the manuscript. This research is partially supported by Ministerio de Ciencia, Innovacion y Universidades, Proyecto PGC2018-096872-B-I00 and by Generalitat Valenciana, Proyecto CIAICO/2021/163. The first-named author is also supported by the National Nature Science Fund of China (No. 12071181) and by Proyecto UJI-B2019-03.Springer-VerlagDepartamento de Matemática AplicadaInstituto Universitario de Matemática Pura y AplicadaEscuela Técnica Superior de Ingeniería IndustrialUniversitat Jaume IAgencia Estatal de InvestigaciónNational Natural Science Foundation of ChinaConselleria d'Educació, Investigació, Cultura i Esport de la Generalitat ValencianaRepositorio Institucional de la Universitat Politècnica de València Riunet20222022-12-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/194638reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PGC2018-096872-B-I00 GRUPOS, ESTRUCTURA LOCAL-GLOBAL E INVARIANTES NUMERICOSGeneralitat Valenciana https://doi.org/10.13039/501100003359 CIAICO%2F2021%2F163 Representaciones y clases de conjugación en grupos finitos: estructura local-globalNational Natural Science Foundation of China https://doi.org/10.13039/501100001809 12071181Universitat Jaume I https://doi.org/10.13039/501100004834 UJI-B2019-03Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 PGC2018-096872-B-I00 GRUPOS, ESTRUCTURA LOCAL-GLOBAL E INVARIANTES NUMERICOSopen accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1946382026-06-13T07:49:27Z
dc.title.none.fl_str_mv An Arad and Fisman&apos
s theorem on products of conjugacy classes revisited
title An Arad and Fisman&apos
spellingShingle An Arad and Fisman&apos
Beltrán Felip, Antonio
Conjugacy classes
Products of conjugacy classes
Solvability criterium
MATEMATICA APLICADA
title_short An Arad and Fisman&apos
title_full An Arad and Fisman&apos
title_fullStr An Arad and Fisman&apos
title_full_unstemmed An Arad and Fisman&apos
title_sort An Arad and Fisman&apos
dc.creator.none.fl_str_mv Beltrán Felip, Antonio
Melchor, Carmen
Felipe Román, María Josefa|||0000-0002-6699-3135
author Beltrán Felip, Antonio
author_facet Beltrán Felip, Antonio
Melchor, Carmen
Felipe Román, María Josefa|||0000-0002-6699-3135
author_role author
author2 Melchor, Carmen
Felipe Román, María Josefa|||0000-0002-6699-3135
author2_role author
author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Instituto Universitario de Matemática Pura y Aplicada
Escuela Técnica Superior de Ingeniería Industrial
Universitat Jaume I
Agencia Estatal de Investigación
National Natural Science Foundation of China
Conselleria d'Educació, Investigació, Cultura i Esport de la Generalitat Valenciana
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Conjugacy classes
Products of conjugacy classes
Solvability criterium
MATEMATICA APLICADA
topic Conjugacy classes
Products of conjugacy classes
Solvability criterium
MATEMATICA APLICADA
description [EN] A theorem of Z. Arad and E. Fisman establishes that if A and B are two non-trivial conjugacy classes of a finite group G such that either AB = A boolean OR B or AB = A(-1) boolean OR B, then G cannot be a non-abelian simple group. We demonstrate that, in fact, < A > = < B > is solvable, the elements of A and B are p-elements for some prime p, and < A > is p-nilpotent. Moreover, under the second assumption, it turns out that A = B. This research is done by appealing to recently developed techniques and results that are based on the Classification of Finite Simple Groups.
publishDate 2022
dc.date.none.fl_str_mv 2022
2022-12-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://riunet.upv.es/handle/10251/194638
url https://riunet.upv.es/handle/10251/194638
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PGC2018-096872-B-I00 GRUPOS, ESTRUCTURA LOCAL-GLOBAL E INVARIANTES NUMERICOS
Generalitat Valenciana https://doi.org/10.13039/501100003359 CIAICO%2F2021%2F163 Representaciones y clases de conjugación en grupos finitos: estructura local-global
National Natural Science Foundation of China https://doi.org/10.13039/501100001809 12071181
Universitat Jaume I https://doi.org/10.13039/501100004834 UJI-B2019-03
Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 PGC2018-096872-B-I00 GRUPOS, ESTRUCTURA LOCAL-GLOBAL E INVARIANTES NUMERICOS
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reconocimiento (by)
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Springer-Verlag
publisher.none.fl_str_mv Springer-Verlag
dc.source.none.fl_str_mv reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
instname:Universitat Politècnica de València (UPV)
instname_str Universitat Politècnica de València (UPV)
reponame_str RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
collection RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15,300719

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