The number of maximal subgroups and probabilistic generation of finite groups

[EN] In this survey we present some significant bounds for the number of maximal subgroups of a given index of a finite group. As a consequence, new bounds for the number of random generators needed to generate a finite d-generated group with high probability which are significantly tighter than the...

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Autores: Ballester-Bolinches, Adolfo, Esteban Romero, Ramón, Jiménez-Seral, Paz, Meng, Hangyang
Tipo de recurso: artículo
Fecha de publicación:2020
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:10251/169538
Acceso en línea:https://riunet.upv.es/handle/10251/169538
Access Level:acceso abierto
Palabra clave:Finite group
Maximal subgroup
Probabilistic generation
Primitive group
MATEMATICA APLICADA
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spelling The number of maximal subgroups and probabilistic generation of finite groupsBallester-Bolinches, AdolfoEsteban Romero, RamónJiménez-Seral, PazMeng, HangyangFinite groupMaximal subgroupProbabilistic generationPrimitive groupMATEMATICA APLICADA[EN] In this survey we present some significant bounds for the number of maximal subgroups of a given index of a finite group. As a consequence, new bounds for the number of random generators needed to generate a finite d-generated group with high probability which are significantly tighter than the ones obtained in the paper of Jaikin-Zapirain and Pyber (Random generation of finite and profinite groups and group enumeration, Ann. Math., 183 (2011) 769-814) are obtained. The results of Jaikin-Zapirain and Pyber, as well as other results of Lubotzky, Detomi, and Lucchini, appear as particular cases of our theorems.This work has been supported by the research grants MTM2014-54707-C3-1-P from the Ministerio de Economa y Competitividad (Spanish Government) and FEDER (European Union) and PRO-METEO/2017/057 from Generalitat (Valencian Community, Spain). The fourth author has been supported by the grant number 201606890006 of the China Scholarship Council.University of IsfahanGeneralitat ValencianaChina Scholarship CouncilEuropean Regional Development FundMinisterio de Economía y CompetitividadRepositorio Institucional de la Universitat Politècnica de València Riunet20202020-03-01journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://riunet.upv.es/handle/10251/169538reponame:RiuNet. Repositorio Institucional de la Universitat Politécnica de Valénciainstname:Universitat Politècnica de València (UPV)InglésengGeneralitat Valenciana https://doi.org/10.13039/501100003359 PROMETEO%2F2017%2F057Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2014-54707-C3-1-P PROPIEDADES ARITMETICAS Y ESTRUCTURALES DE GRUPOS Y SEMIGRUPOS IChina Scholarship Council https://doi.org/10.13039/501100004543 201606890006open accesshttp://purl.org/coar/access_right/c_abf2Reconocimiento (by)http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:riunet.upv.es:10251/1695382026-06-13T07:49:27Z
dc.title.none.fl_str_mv The number of maximal subgroups and probabilistic generation of finite groups
title The number of maximal subgroups and probabilistic generation of finite groups
spellingShingle The number of maximal subgroups and probabilistic generation of finite groups
Ballester-Bolinches, Adolfo
Finite group
Maximal subgroup
Probabilistic generation
Primitive group
MATEMATICA APLICADA
title_short The number of maximal subgroups and probabilistic generation of finite groups
title_full The number of maximal subgroups and probabilistic generation of finite groups
title_fullStr The number of maximal subgroups and probabilistic generation of finite groups
title_full_unstemmed The number of maximal subgroups and probabilistic generation of finite groups
title_sort The number of maximal subgroups and probabilistic generation of finite groups
dc.creator.none.fl_str_mv Ballester-Bolinches, Adolfo
Esteban Romero, Ramón
Jiménez-Seral, Paz
Meng, Hangyang
author Ballester-Bolinches, Adolfo
author_facet Ballester-Bolinches, Adolfo
Esteban Romero, Ramón
Jiménez-Seral, Paz
Meng, Hangyang
author_role author
author2 Esteban Romero, Ramón
Jiménez-Seral, Paz
Meng, Hangyang
author2_role author
author
author
dc.contributor.none.fl_str_mv Generalitat Valenciana
China Scholarship Council
European Regional Development Fund
Ministerio de Economía y Competitividad
Repositorio Institucional de la Universitat Politècnica de València Riunet
dc.subject.none.fl_str_mv Finite group
Maximal subgroup
Probabilistic generation
Primitive group
MATEMATICA APLICADA
topic Finite group
Maximal subgroup
Probabilistic generation
Primitive group
MATEMATICA APLICADA
description [EN] In this survey we present some significant bounds for the number of maximal subgroups of a given index of a finite group. As a consequence, new bounds for the number of random generators needed to generate a finite d-generated group with high probability which are significantly tighter than the ones obtained in the paper of Jaikin-Zapirain and Pyber (Random generation of finite and profinite groups and group enumeration, Ann. Math., 183 (2011) 769-814) are obtained. The results of Jaikin-Zapirain and Pyber, as well as other results of Lubotzky, Detomi, and Lucchini, appear as particular cases of our theorems.
publishDate 2020
dc.date.none.fl_str_mv 2020
2020-03-01
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/10251/169538
url https://riunet.upv.es/handle/10251/169538
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%2F2017%2F057
Ministerio de Economía y Competitividad http://dx.doi.org/10.13039/501100003329 MTM2014-54707-C3-1-P PROPIEDADES ARITMETICAS Y ESTRUCTURALES DE GRUPOS Y SEMIGRUPOS I
China Scholarship Council https://doi.org/10.13039/501100004543 201606890006
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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score 15,300724

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