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On finite groups with many supersoluble subgroups

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On finite groups with many supersoluble subgroups

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dc.contributor.author Ballester-Bolinches, A. es_ES
dc.contributor.author Esteban Romero, Ramón es_ES
dc.contributor.author Lu, Jiakuan es_ES
dc.date.accessioned 2020-10-14T03:30:51Z
dc.date.available 2020-10-14T03:30:51Z
dc.date.issued 2017 es_ES
dc.identifier.issn 0003-889X es_ES
dc.identifier.uri http://hdl.handle.net/10251/151655
dc.description.abstract [EN] The solubility of a finite group with less than 6 non-supersoluble subgroups is confirmed in the paper. Moreover we prove that a finite insoluble group has exactly 6 non-supersoluble subgroups if and only if it is isomorphic to A5 or SL2 (5). Furthermore, it is shown that a finite insoluble group has exactly 22 non-nilpotent subgroups if and only if it is isomorphic to A5 or SL2 (5). This confirms a conjecture of Zarrin (Arch Math (Basel) 99:201 206, 2012). es_ES
dc.description.sponsorship The first and second author are supported by the Grant MTM2014-54707-C3-1-P from the Ministerio de Economia y Competitividad, Spain, and FEDER, European Union. The first author is supported by the National Natural Science Foundation of China (11271085) and a Project of Natural Science Foundation of Guangdong Province (2015A030313791). The third author is supported by the National Natural Science Foundation of China (11461007), and the Guangxi Natural Science Foundation Program (2016GXNSFAA380156). This research has been done during a visit of the third author to the Departament de Matematiques of the Universitat de Valencia. He expresses his gratitude to this institution. We thank the anonymous referee for his/her comments that have helped us to improve the presentation of the paper. es_ES
dc.language Inglés es_ES
dc.publisher Springer-Verlag es_ES
dc.relation.ispartof Archiv der Mathematik es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Finite group es_ES
dc.subject Supersoluble subgroup es_ES
dc.subject Soluble group es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title On finite groups with many supersoluble subgroups es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s00013-017-1041-4 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/Natural Science Foundation of Guangdong Province//2015A030313791/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/MINECO//MTM2014-54707-C3-1-P/ES/PROPIEDADES ARITMETICAS Y ESTRUCTURALES DE GRUPOS Y SEMIGRUPOS I/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/NSFC//11461007/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/NSFC//11271085/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/Natural Science Foundation of Guangxi Province//2016GXNSFAA380156/ es_ES
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Ballester-Bolinches, A.; Esteban Romero, R.; Lu, J. (2017). On finite groups with many supersoluble subgroups. Archiv der Mathematik. 109(1):3-8. https://doi.org/10.1007/s00013-017-1041-4 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1007/s00013-017-1041-4 es_ES
dc.description.upvformatpinicio 3 es_ES
dc.description.upvformatpfin 8 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 109 es_ES
dc.description.issue 1 es_ES
dc.relation.pasarela S\336141 es_ES
dc.contributor.funder National Natural Science Foundation of China es_ES
dc.contributor.funder Natural Science Foundation of Guangxi Province es_ES
dc.contributor.funder Natural Science Foundation of Guangdong Province es_ES
dc.contributor.funder Ministerio de Economía y Competitividad es_ES
dc.description.references J. Bray, D. Holt, and C. Roney-Dougal, The maximal subgroups of the low-dimensional finite classical groups, London Math. Soc. Lect. Note Ser. Cambridge Univ. Press, Cambridge, UK, 2013. es_ES
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dc.description.references M. Zarrin, A generalization of Schmidt’s theorem on groups with all subgroups nilpotent, Arch. Math. (Basel) 99 (2012), 201–206. es_ES


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