p-divisibility of conjugacy class sizes and normal p-complements

. Let N be a normal subgroup of a group G and let p be a prime. We prove that if the p-part of jx Gj is a constant for every prime-power order element x 2 N n Z.N /, then N is solvable and has normal p-complement.

Detalhes bibliográficos
Autores: Beltrán, Antonio, Shao, Changguo, Felipe Román, María Josefa|||0000-0002-6699-3135
Formato: artículo
Fecha de publicación:2015
País:España
Recursos:Universitat Politècnica de València (UPV)
Repositorio:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Idioma:inglés
OAI Identifier:oai:riunet.upv.es:10251/64392
Acesso em linha:https://riunet.upv.es/handle/10251/64392
Access Level:acceso abierto
Palavra-chave:Finite groups
Conjugacy class sizes
Normal subgroups
Prime-power order elements
MATEMATICA APLICADA
id ES_7e47b7df8ca871ea986f64c200d5c670
oai_identifier_str oai:riunet.upv.es:10251/64392
network_acronym_str ES
network_name_str España
repository_id_str
spelling p-divisibility of conjugacy class sizes and normal p-complementsBeltrán, AntonioShao, ChangguoFelipe Román, María Josefa|||0000-0002-6699-3135Finite groupsConjugacy class sizesNormal subgroupsPrime-power order elementsMATEMATICA APLICADA. Let N be a normal subgroup of a group G and let p be a prime. We prove that if the p-part of jx Gj is a constant for every prime-power order element x 2 N n Z.N /, then N is solvable and has normal p-complement.This research is supported by the Valencian Government, Proyecto PROMETEO/2011/30, and by the Spanish Government, Proyecto MTM2010-19938-C03-02. The third author is supported by the research Project NNSF of China (Grant No. 11201401 and No. 11301218) and University of Jinan Research Funds for Doctors (XBS1335 and XBS1336).De GruyterDepartamento de Matemática AplicadaInstituto Universitario de Matemática Pura y AplicadaEscuela Técnica Superior de Ingeniería IndustrialMinisterio de Ciencia e InnovaciónGeneralitat ValencianaUniversity of JinanNational Natural Science Foundation of ChinaRepositorio Institucional de la Universitat Politècnica de València Riunet20152015-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/64392reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengGeneralitat Valenciana https://doi.org/10.13039/501100003359 PROMETEO%2F2011%2F030National Natural Science Foundation of China https://doi.org/10.13039/501100001809 11201401Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2010-19938-C03-02 PROPIEDADES ARITMETICAS Y ESTRUCTURALES DE LOS GRUPOS. APLICACIONES. IIIUJN UJN XBS1335National Natural Science Foundation of China https://doi.org/10.13039/501100001809 11301218UJN UJN XBS1336open 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:10251/643922026-06-13T07:49:27Z
dc.title.none.fl_str_mv p-divisibility of conjugacy class sizes and normal p-complements
title p-divisibility of conjugacy class sizes and normal p-complements
spellingShingle p-divisibility of conjugacy class sizes and normal p-complements
Beltrán, Antonio
Finite groups
Conjugacy class sizes
Normal subgroups
Prime-power order elements
MATEMATICA APLICADA
title_short p-divisibility of conjugacy class sizes and normal p-complements
title_full p-divisibility of conjugacy class sizes and normal p-complements
title_fullStr p-divisibility of conjugacy class sizes and normal p-complements
title_full_unstemmed p-divisibility of conjugacy class sizes and normal p-complements
title_sort p-divisibility of conjugacy class sizes and normal p-complements
dc.creator.none.fl_str_mv Beltrán, Antonio
Shao, Changguo
Felipe Román, María Josefa|||0000-0002-6699-3135
author Beltrán, Antonio
author_facet Beltrán, Antonio
Shao, Changguo
Felipe Román, María Josefa|||0000-0002-6699-3135
author_role author
author2 Shao, Changguo
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
Ministerio de Ciencia e Innovación
Generalitat Valenciana
University of Jinan
National Natural Science Foundation of China
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Finite groups
Conjugacy class sizes
Normal subgroups
Prime-power order elements
MATEMATICA APLICADA
topic Finite groups
Conjugacy class sizes
Normal subgroups
Prime-power order elements
MATEMATICA APLICADA
description . Let N be a normal subgroup of a group G and let p be a prime. We prove that if the p-part of jx Gj is a constant for every prime-power order element x 2 N n Z.N /, then N is solvable and has normal p-complement.
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-01-01
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/10251/64392
url https://riunet.upv.es/handle/10251/64392
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
National Natural Science Foundation of China https://doi.org/10.13039/501100001809 11201401
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
UJN UJN XBS1335
National Natural Science Foundation of China https://doi.org/10.13039/501100001809 11301218
UJN UJN XBS1336
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 De Gruyter
publisher.none.fl_str_mv De Gruyter
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
_version_ 1869411724675776512
score 15.301603

Registos relacionados