Solvability of normal subgroups and G-class sizes

[EN] We study the solvability of a normal subgroup N of a finite group G having exactly three G-conjugacy class sizes. We show that if the set of G-class sizes of N is {1, m, mpa }, with p a prime not dividing m, then N is solvable. Thus, we get a partial extension for normal subgroups on N. Itˆo’s...

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Autores: Beltrán, Antonio, Felipe Román, María Josefa|||0000-0002-6699-3135
Tipo de recurso: artículo
Fecha de publicación:2013
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:10251/68264
Acceso en línea:https://riunet.upv.es/handle/10251/68264
Access Level:acceso abierto
Palabra clave:Finite groups
Conjugacy class sizes
Solvable groups
MATEMATICA APLICADA
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spelling Solvability of normal subgroups and G-class sizesBeltrán, AntonioFelipe Román, María Josefa|||0000-0002-6699-3135Finite groupsConjugacy class sizesSolvable groupsMATEMATICA APLICADA[EN] We study the solvability of a normal subgroup N of a finite group G having exactly three G-conjugacy class sizes. We show that if the set of G-class sizes of N is {1, m, mpa }, with p a prime not dividing m, then N is solvable. Thus, we get a partial extension for normal subgroups on N. Itˆo’s theorem on the solvability of groups having exactly three class sizes.This research is supported by the Valencian Government, Proyecto PROMETEO/2011/30, by the Spanish Government, Proyecto MTM2010-19938-C03-02 and the first author is also supported by grant Fundaci´o Bancaixa P11B2010-47. The second author would like to thank the members of the Institute of Mathematics at the University of Aberdeen for their warm hospitality and for many helpful discussions during her visit to this University.Debreceni egyetem matematika intézetDepartamento de Matemática AplicadaInstituto Universitario de Matemática Pura y AplicadaEscuela Técnica Superior de Ingeniería IndustrialGeneralitat ValencianaFundación BancajaMinisterio de Ciencia e InnovaciónUniversitat Jaume IRepositorio Institucional de la Universitat Politècnica de València Riunet20132013-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/68264reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengGeneralitat Valenciana https://doi.org/10.13039/501100003359 PROMETEO%2F2011%2F030Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2010-19938-C03-02 PROPIEDADES ARITMETICAS Y ESTRUCTURALES DE LOS GRUPOS. APLICACIONES. IIIUniversitat Jaume I https://doi.org/10.13039/501100004834 P1·1B2010-47open accesshttp://purl.org/coar/access_right/c_abf2Reserva de todos los derechoshttp://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/682642026-06-13T07:49:27Z
dc.title.none.fl_str_mv Solvability of normal subgroups and G-class sizes
title Solvability of normal subgroups and G-class sizes
spellingShingle Solvability of normal subgroups and G-class sizes
Beltrán, Antonio
Finite groups
Conjugacy class sizes
Solvable groups
MATEMATICA APLICADA
title_short Solvability of normal subgroups and G-class sizes
title_full Solvability of normal subgroups and G-class sizes
title_fullStr Solvability of normal subgroups and G-class sizes
title_full_unstemmed Solvability of normal subgroups and G-class sizes
title_sort Solvability of normal subgroups and G-class sizes
dc.creator.none.fl_str_mv Beltrán, Antonio
Felipe Román, María Josefa|||0000-0002-6699-3135
author Beltrán, Antonio
author_facet Beltrán, Antonio
Felipe Román, María Josefa|||0000-0002-6699-3135
author_role author
author2 Felipe Román, María Josefa|||0000-0002-6699-3135
author2_role author
dc.contributor.none.fl_str_mv Departamento de Matemática Aplicada
Instituto Universitario de Matemática Pura y Aplicada
Escuela Técnica Superior de Ingeniería Industrial
Generalitat Valenciana
Fundación Bancaja
Ministerio de Ciencia e Innovación
Universitat Jaume I
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Finite groups
Conjugacy class sizes
Solvable groups
MATEMATICA APLICADA
topic Finite groups
Conjugacy class sizes
Solvable groups
MATEMATICA APLICADA
description [EN] We study the solvability of a normal subgroup N of a finite group G having exactly three G-conjugacy class sizes. We show that if the set of G-class sizes of N is {1, m, mpa }, with p a prime not dividing m, then N is solvable. Thus, we get a partial extension for normal subgroups on N. Itˆo’s theorem on the solvability of groups having exactly three class sizes.
publishDate 2013
dc.date.none.fl_str_mv 2013
2013-01-01
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/10251/68264
url https://riunet.upv.es/handle/10251/68264
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Generalitat Valenciana https://doi.org/10.13039/501100003359 PROMETEO%2F2011%2F030
Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2010-19938-C03-02 PROPIEDADES ARITMETICAS Y ESTRUCTURALES DE LOS GRUPOS. APLICACIONES. III
Universitat Jaume I https://doi.org/10.13039/501100004834 P1·1B2010-47
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
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
Reserva de todos los derechos
http://rightsstatements.org/vocab/InC/1.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Debreceni egyetem matematika intézet
publisher.none.fl_str_mv Debreceni egyetem matematika intézet
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 15.301603

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