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
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/38548
Title:
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A reduction theorem for a conjecture on products of two ¿-decomposable groups
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Author:
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Kazarin, L. S.
Martínez Pastor, Ana
Perez Ramos, Maria Dolores
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UPV Unit:
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Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
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Issued date:
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Abstract:
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[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 ...[+]
[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.
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Subjects:
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Finite groups
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pi-structure
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pi-decomposable groups
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Products of subgroups
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Hall subgroups
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Copyrigths:
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Reserva de todos los derechos
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Source:
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Journal of Algebra. (issn:
0021-8693
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DOI:
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10.1016/j.jalgebra.2013.01.017
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Publisher:
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Elsevier
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Publisher version:
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http://dx.doi.org/10.1016/j.jalgebra.2013.01.017
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Project ID:
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MINECO/MTM2010-19938-C03-02
RFBR/13-01-00469
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Thanks:
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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 ...[+]
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.
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Type:
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Artículo
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