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A reduction theorem for a conjecture on products of two ¿-decomposable groups

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A reduction theorem for a conjecture on products of two ¿-decomposable groups

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dc.contributor.author Kazarin, L. S. es_ES
dc.contributor.author Martínez Pastor, Ana es_ES
dc.contributor.author Perez Ramos, Maria Dolores es_ES
dc.date.accessioned 2014-07-03T10:50:40Z
dc.date.issued 2013-04-01
dc.identifier.issn 0021-8693
dc.identifier.uri http://hdl.handle.net/10251/38548
dc.description.abstract [EN] For a set of primes pi, a group X is said to be pi-decomposable if X = X-pi x X-pi' is the direct product of a pi-subgroup X-pi and a pi'-subgroup X-pi', where pi' is the complementary of pi in the set of all prime numbers. The main result of this paper is a reduction theorem for the following conjecture: "Let pi be a set of odd primes. If the finite group G = AB is a product of two pi-decomposable subgroups A = A(pi) x A(pi') and B = B-pi x B-pi', then A(pi)B(pi) = B(pi)A(pi) and this is a Hall pi-subgroup of G." We establish that a minimal counterexample to this conjecture is an almost simple group. The conjecture is then achieved in a forthcoming paper. (C) 2013 Elsevier Inc. All rights reserved. es_ES
dc.description.sponsorship The second and third author have been supported by Proyecto MTM2010-19938-C03-02, Ministerio de Economia y Competitividad, Spain. The first author would like to thank the Universitat de Valencia and the Universitat Politecnica de Valencia for their warm hospitality during the preparation of this paper. He has been also supported by RFBR project 13-01-00469.
dc.format.extent 13 es_ES
dc.language Inglés es_ES
dc.publisher Elsevier es_ES
dc.relation MINECO/MTM2010-19938-C03-02 es_ES
dc.relation RFBR/13-01-00469 es_ES
dc.relation.ispartof Journal of Algebra es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Finite groups es_ES
dc.subject pi-structure es_ES
dc.subject pi-decomposable groups es_ES
dc.subject Products of subgroups es_ES
dc.subject Hall subgroups es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.title A reduction theorem for a conjecture on products of two ¿-decomposable groups es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1016/j.jalgebra.2013.01.017
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 Kazarin, LS.; Martínez Pastor, A.; Perez Ramos, MD. (2013). A reduction theorem for a conjecture on products of two ¿-decomposable groups. Journal of Algebra. 379:301-313. doi:10.1016/j.jalgebra.2013.01.017 es_ES
dc.description.accrualMethod S es_ES
dc.relation.publisherversion http://dx.doi.org/10.1016/j.jalgebra.2013.01.017 es_ES
dc.description.upvformatpinicio 301 es_ES
dc.description.upvformatpfin 313 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 379 es_ES
dc.relation.senia 246325
dc.contributor.funder Ministerio de Economía y Competitividad
dc.contributor.funder Russian Science Foundation


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