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Thompson-like characterization of solubility for products of finite groups

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Thompson-like characterization of solubility for products of finite groups

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dc.contributor.author Hauck, P. es_ES
dc.contributor.author Kazarin, L. S. es_ES
dc.contributor.author Martínez-Pastor, Ana es_ES
dc.contributor.author Pérez-Ramos, M. D. es_ES
dc.date.accessioned 2022-09-30T18:06:39Z
dc.date.available 2022-09-30T18:06:39Z
dc.date.issued 2021-02 es_ES
dc.identifier.issn 0373-3114 es_ES
dc.identifier.uri http://hdl.handle.net/10251/186784
dc.description.abstract [EN] A remarkable result of Thompson states that a finite group is soluble if and only if all its two-generated subgroups are soluble. This result has been generalized in numerous ways, and it is in the core of a wide area of research in the theory of groups, aiming for global properties of groups from local properties of two-generated (or more generally, n-generated) subgroups. We contribute an extension of Thompson's theorem from the perspective of factorized groups. More precisely, we study finite groups G = AB with subgroups A, B such that < a, b > is soluble for all a is an element of A and b is an element of B. In this case, the group G is said to be an S-connected product of the subgroups A and B for the class S of all finite soluble groups. Our Main Theorem states that G = AB is S-connected if and only if [A, B] is soluble. In the course of the proof, we derive a result about independent primes regarding the soluble graph of almost simple groups that might be interesting in its own right. es_ES
dc.description.sponsorship Research supported by Proyectos PROMETEO/2017/057 from the Generalitat Valenciana (Valencian Community, Spain) and PGC2018-096872-B-I00 from the Ministerio de Ciencia, Innovacion y Universidades, Spain, and FEDER, European Union; and second author also by Project VIP-008 of Yaroslavl P. Demidov State University. es_ES
dc.language Inglés es_ES
dc.publisher Springer-Verlag es_ES
dc.relation.ispartof Annali di Matematica Pura ed Applicata (1923 -) es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Solubility es_ES
dc.subject Products of subgroups es_ES
dc.subject Two-generated subgroups es_ES
dc.subject S-connection es_ES
dc.subject Almost simple groups es_ES
dc.subject Independent primes es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Thompson-like characterization of solubility for products of finite groups es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1007/s10231-020-00998-z es_ES
dc.relation.projectID info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PGC2018-096872-B-I00/ES/GRUPOS, ESTRUCTURA LOCAL-GLOBAL E INVARIANTES NUMERICOS/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/P.G. Demidov Yaroslavl State University//VIP-008/ es_ES
dc.relation.projectID info:eu-repo/grantAgreement/Generalitat Valenciana//Prometeo%2F2017%2F057//Grupos y semigrupos: estructura y aplicaciones/ 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.contributor.affiliation Universitat Politècnica de València. Instituto Universitario de Matemática Pura y Aplicada - Institut Universitari de Matemàtica Pura i Aplicada es_ES
dc.description.bibliographicCitation Hauck, P.; Kazarin, LS.; Martínez-Pastor, A.; Pérez-Ramos, MD. (2021). Thompson-like characterization of solubility for products of finite groups. Annali di Matematica Pura ed Applicata (1923 -). 200(1):337-362. https://doi.org/10.1007/s10231-020-00998-z es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.1007/s10231-020-00998-z es_ES
dc.description.upvformatpinicio 337 es_ES
dc.description.upvformatpfin 362 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 200 es_ES
dc.description.issue 1 es_ES
dc.relation.pasarela S\418260 es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder AGENCIA ESTATAL DE INVESTIGACION es_ES
dc.contributor.funder European Regional Development Fund es_ES
dc.contributor.funder P.G. Demidov Yaroslavl State University es_ES
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