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Products of finite connected subgroups

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Products of finite connected subgroups

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dc.contributor.author Gallego, María Pilar es_ES
dc.contributor.author Hauck, Peter es_ES
dc.contributor.author Kazarin, Lev S. es_ES
dc.contributor.author Martínez-Pastor, Ana es_ES
dc.contributor.author Pérez-Ramos, María Dolores es_ES
dc.date.accessioned 2021-09-11T03:31:21Z
dc.date.available 2021-09-11T03:31:21Z
dc.date.issued 2020-09 es_ES
dc.identifier.uri http://hdl.handle.net/10251/172145
dc.description.abstract [EN] For a non-empty class of groups L, a finite group G = AB is said to be an L-connected product of the subgroups A and B if < a, b > is an element of L for all a is an element of A and b is an element of B. In a previous paper, we prove that, for such a product, when L = S is the class of finite soluble groups, then [A, B] is soluble. This generalizes the theorem of Thompson that states the solubility of finite groups whose two-generated subgroups are soluble. In the present paper, our result is applied to extend to finite groups previous research about finite groups in the soluble universe. In particular, we characterize connected products for relevant classes of groups, among others, the class of metanilpotent groups and the class of groups with nilpotent derived subgroup. Additionally, we give local descriptions of relevant subgroups of finite groups. 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 third author also by Project VIP-008 of Yaroslavl P. Demidov State University. es_ES
dc.language Inglés es_ES
dc.publisher MDPI AG es_ES
dc.relation.ispartof Mathematics es_ES
dc.rights Reconocimiento (by) es_ES
dc.subject Finite groups es_ES
dc.subject Products of subgroups es_ES
dc.subject Two-generated subgroups es_ES
dc.subject L-connection es_ES
dc.subject Fitting classes es_ES
dc.subject Fitting series es_ES
dc.subject Formations es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title Products of finite connected subgroups es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.3390/math8091498 es_ES
dc.relation.projectID info:eu-repo/grantAgreement/GVA//PROMETEO%2F2017%2F057/ 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.rights.accessRights Abierto 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.contributor.affiliation Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada es_ES
dc.description.bibliographicCitation Gallego, MP.; Hauck, P.; Kazarin, LS.; Martínez-Pastor, A.; Pérez-Ramos, MD. (2020). Products of finite connected subgroups. Mathematics. 8(9):1-8. https://doi.org/10.3390/math8091498 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion https://doi.org/10.3390/math8091498 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 8 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 8 es_ES
dc.description.issue 9 es_ES
dc.identifier.eissn 2227-7390 es_ES
dc.relation.pasarela S\417838 es_ES
dc.contributor.funder Generalitat Valenciana es_ES
dc.contributor.funder Agencia Estatal de Investigación es_ES
dc.contributor.funder European Regional Development Fund es_ES
dc.description.references Hauck, P., Kazarin, L. S., Martínez-Pastor, A., & Pérez-Ramos, M. D. (2020). Thompson-like characterization of solubility for products of finite groups. Annali di Matematica Pura ed Applicata (1923 -), 200(1), 337-362. doi:10.1007/s10231-020-00998-z es_ES
dc.description.references Thompson, J. G. (1968). Nonsolvable finite groups all of whose local subgroups are solvable. Bulletin of the American Mathematical Society, 74(3), 383-437. doi:10.1090/s0002-9904-1968-11953-6 es_ES
dc.description.references Flavell, P. (1995). Finite groups in which every two elements generate a soluble subgroup. Inventiones Mathematicae, 121(1), 279-285. doi:10.1007/bf01884299 es_ES
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dc.description.references Gállego, M. P., Hauck, P., & Pérez-Ramos, M. D. (2008). Soluble products of connected subgroups. Revista Matemática Iberoamericana, 433-461. doi:10.4171/rmi/542 es_ES
dc.description.references Gállego, M. P., Hauck, P., & Pérez-Ramos, M. D. (2008). On 2-generated subgroups and products of groups. Journal of Group Theory, 11(6). doi:10.1515/jgt.2008.054 es_ES
dc.description.references Gállego, M. P., Hauck, P., & Pérez-Ramos, M. D. (2011). Saturated formations and products of connected subgroups. Journal of Algebra, 333(1), 105-119. doi:10.1016/j.jalgebra.2010.09.012 es_ES
dc.description.references Gállego, M. P., Hauck, P., & Pérez-Ramos, M. D. (2016). 2-Engel relations between subgroups. Journal of Algebra, 447, 31-55. doi:10.1016/j.jalgebra.2015.08.030 es_ES
dc.description.references GRUNEWALD, F., KUNYAVSKII, B., & PLOTKIN, E. (2013). CHARACTERIZATION OF SOLVABLE GROUPS AND SOLVABLE RADICAL. International Journal of Algebra and Computation, 23(05), 1011-1062. doi:10.1142/s0218196713300016 es_ES
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dc.description.references Gross, F. (1973). Finite groups which are the product of two nilpotent subgroups. Bulletin of the Australian Mathematical Society, 9(2), 267-274. doi:10.1017/s0004972700043161 es_ES


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