Class sizes of prime-power order p&apos

We prove an extension of the renowned Itô’s theorem on groups having two class sizes in three different directions at the same time: normal subgroups, p′p′-elements and prime-power order elements. Let NN be a normal subgroup of a finite group GG and let pp be a fixed prime. Suppose that |xG|=1|xG|=1...

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Authors: Beltrán, Antonio, Shao, Changguo, Felipe Román, María Josefa|||0000-0002-6699-3135
Format: article
Publication Date:2015
Country:España
Institution:Universitat Politècnica de València (UPV)
Repository:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia
Language:English
OAI Identifier:oai:riunet.upv.es:10251/64385
Online Access:https://riunet.upv.es/handle/10251/64385
Access Level:Open access
Keyword:Finite groups
Conjugacy class sizes
Normal subgroups
Prime-power order element
p Elements
MATEMATICA APLICADA
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spelling Class sizes of prime-power order p&apos-elements and normal subgroupsBeltrán, AntonioShao, ChangguoFelipe Román, María Josefa|||0000-0002-6699-3135Finite groupsConjugacy class sizesNormal subgroupsPrime-power order elementp ElementsMATEMATICA APLICADAWe prove an extension of the renowned Itô’s theorem on groups having two class sizes in three different directions at the same time: normal subgroups, p′p′-elements and prime-power order elements. Let NN be a normal subgroup of a finite group GG and let pp be a fixed prime. Suppose that |xG|=1|xG|=1 or mm for every qq-element of NN and for every prime q≠pq≠p. Then, NN has nilpotent pp-complements.We are very grateful to the referee, who provided us a significant simplification of the last step of the proof of the main theorem and for many comments which have contributed to improve the paper. C. G. Shao wants to express his deep gratitude for the warm hospitality he has received in the Departamento de Matematicas of the Universidad Jaume I in Castellon, Spain. This research is supported by the Valencian Government, Proyecto PROMETEO/2011/30, by the Spanish Government, Proyecto MTM2010-19938-C03-02. The third author is supported by the research Project NNSF of China (Grant Nos. 11201401 and 11301218) and University of Jinan Research Funds for Doctors (XBS1335 and XBS1336).Springer Verlag (Germany)Departamento de Matemática AplicadaInstituto Universitario de Matemática Pura y AplicadaEscuela Técnica Superior de Ingeniería IndustrialMinisterio de Ciencia e InnovaciónUniversity of JinanNational Natural Science Foundation of ChinaGeneralitat ValencianaRepositorio Institucional de la Universitat Politècnica de València Riunet20152015-10-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfapplication/pdfhttps://riunet.upv.es/handle/10251/64385reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengGeneralitat Valenciana https://doi.org/10.13039/501100003359 PROMETEO%2F2011%2F030UJN UJN XBS1335Ministerio de Ciencia e Innovación http://dx.doi.org/10.13039/501100004837 MTM2010-19938-C03-02 PROPIEDADES ARITMETICAS Y ESTRUCTURALES DE LOS GRUPOS. APLICACIONES. IIINational Natural Science Foundation of China https://doi.org/10.13039/501100001809 11201401National 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:10251/643852026-06-13T07:49:27Z
dc.title.none.fl_str_mv Class sizes of prime-power order p&apos
-elements and normal subgroups
title Class sizes of prime-power order p&apos
spellingShingle Class sizes of prime-power order p&apos
Beltrán, Antonio
Finite groups
Conjugacy class sizes
Normal subgroups
Prime-power order element
p Elements
MATEMATICA APLICADA
title_short Class sizes of prime-power order p&apos
title_full Class sizes of prime-power order p&apos
title_fullStr Class sizes of prime-power order p&apos
title_full_unstemmed Class sizes of prime-power order p&apos
title_sort Class sizes of prime-power order p&apos
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
University of Jinan
National Natural Science Foundation of China
Generalitat Valenciana
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 element
p Elements
MATEMATICA APLICADA
topic Finite groups
Conjugacy class sizes
Normal subgroups
Prime-power order element
p Elements
MATEMATICA APLICADA
description We prove an extension of the renowned Itô’s theorem on groups having two class sizes in three different directions at the same time: normal subgroups, p′p′-elements and prime-power order elements. Let NN be a normal subgroup of a finite group GG and let pp be a fixed prime. Suppose that |xG|=1|xG|=1 or mm for every qq-element of NN and for every prime q≠pq≠p. Then, NN has nilpotent pp-complements.
publishDate 2015
dc.date.none.fl_str_mv 2015
2015-10-01
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/10251/64385
url https://riunet.upv.es/handle/10251/64385
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
UJN UJN XBS1335
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
National Natural Science Foundation of China https://doi.org/10.13039/501100001809 11201401
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
application/pdf
dc.publisher.none.fl_str_mv Springer Verlag (Germany)
publisher.none.fl_str_mv Springer Verlag (Germany)
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 15,300724

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