Conjugacy classes contained in normal subgroups: an overview

[EN] We survey known results concerning how the conjugacy classes contained in a normal subgroup and their sizes exert an influence on the normal structure of a finite group. The approach is mainly presented in the framework of graphs associated to the conjugacy classes, which have been introduced a...

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Authors: Beltrán, Antonio, Melchor, Carmen, Felipe Román, María Josefa|||0000-0002-6699-3135
Format: article
Publication Date:2018
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:10251/104808
Online Access:https://riunet.upv.es/handle/10251/104808
Access Level:Open access
Keyword:Conjugacy classes
Normal subgroups
Graphs
MATEMATICA APLICADA
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repository_id_str
spelling Conjugacy classes contained in normal subgroups: an overviewBeltrán, AntonioMelchor, CarmenFelipe Román, María Josefa|||0000-0002-6699-3135Conjugacy classesNormal subgroupsGraphsMATEMATICA APLICADA[EN] We survey known results concerning how the conjugacy classes contained in a normal subgroup and their sizes exert an influence on the normal structure of a finite group. The approach is mainly presented in the framework of graphs associated to the conjugacy classes, which have been introduced and developed in the past few years. We will see how the properties of these graphs, along with some extensions of the classic Landau's Theorem on conjugacy classes for normal subgroups, have been used in order to classify groups and normal subgroups satisfying certain conjugacy class numerical conditions.Some of the results of this paper are part of the third author's Ph.D. thesis at the University Jaume I of Castellón, who is financially supported by a predoctoral grant of this university. The first and second authors are supported by the Valencian Government, Proyecto PROMETEOII/2015/011. The first and the third authors are also partially supported by Universitat Jaume I, grant P11B-2015-77.University of IsfahanDepartamento de Matemática AplicadaInstituto Universitario de Matemática Pura y AplicadaEscuela Técnica Superior de Ingeniería IndustrialGeneralitat ValencianaUniversitat Jaume IRepositorio Institucional de la Universitat Politècnica de València Riunet20182018-01-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/104808reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengGeneralitat Valenciana https://doi.org/10.13039/501100003359 PROMETEOII%2F2015%2F011 Caracteres y clases de conjugación de grupos finitos IIUniversitat Jaume I https://doi.org/10.13039/501100004834 P1-1B-2015-77open accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1048082026-06-13T07:49:27Z
dc.title.none.fl_str_mv Conjugacy classes contained in normal subgroups: an overview
title Conjugacy classes contained in normal subgroups: an overview
spellingShingle Conjugacy classes contained in normal subgroups: an overview
Beltrán, Antonio
Conjugacy classes
Normal subgroups
Graphs
MATEMATICA APLICADA
title_short Conjugacy classes contained in normal subgroups: an overview
title_full Conjugacy classes contained in normal subgroups: an overview
title_fullStr Conjugacy classes contained in normal subgroups: an overview
title_full_unstemmed Conjugacy classes contained in normal subgroups: an overview
title_sort Conjugacy classes contained in normal subgroups: an overview
dc.creator.none.fl_str_mv Beltrán, Antonio
Melchor, Carmen
Felipe Román, María Josefa|||0000-0002-6699-3135
author Beltrán, Antonio
author_facet Beltrán, 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
Generalitat Valenciana
Universitat Jaume I
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Conjugacy classes
Normal subgroups
Graphs
MATEMATICA APLICADA
topic Conjugacy classes
Normal subgroups
Graphs
MATEMATICA APLICADA
description [EN] We survey known results concerning how the conjugacy classes contained in a normal subgroup and their sizes exert an influence on the normal structure of a finite group. The approach is mainly presented in the framework of graphs associated to the conjugacy classes, which have been introduced and developed in the past few years. We will see how the properties of these graphs, along with some extensions of the classic Landau's Theorem on conjugacy classes for normal subgroups, have been used in order to classify groups and normal subgroups satisfying certain conjugacy class numerical conditions.
publishDate 2018
dc.date.none.fl_str_mv 2018
2018-01-01
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/10251/104808
url https://riunet.upv.es/handle/10251/104808
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 PROMETEOII%2F2015%2F011 Caracteres y clases de conjugación de grupos finitos II
Universitat Jaume I https://doi.org/10.13039/501100004834 P1-1B-2015-77
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 University of Isfahan
publisher.none.fl_str_mv University of Isfahan
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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