Ballester Bolinches, A.; Cossey, J.; Esteban Romero, R. (2003). On finite groups generated by strongly cosubnormal subgroups. Journal of Algebra. 1(259):226-234. https://doi.org/10.1016/S0021-8693(02)00535-5
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/19004
Title:
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On finite groups generated by strongly cosubnormal subgroups
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Author:
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Ballester Bolinches, Adolfo
Cossey, John
Esteban Romero, Ramón
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UPV Unit:
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Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
Universitat Politècnica de València. Instituto Universitario de Matemática Pura y Aplicada - Institut Universitari de Matemàtica Pura i Aplicada
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Issued date:
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Abstract:
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[EN] Two subgroups A and B of a group G are cosubnormal if A and B are subnormal in their join <A,B> and are strongly cosubnormal if every subgroup of A is cosubnormal with every subgroup of B. We find necessary and ...[+]
[EN] Two subgroups A and B of a group G are cosubnormal if A and B are subnormal in their join <A,B> and are strongly cosubnormal if every subgroup of A is cosubnormal with every subgroup of B. We find necessary and sufficient conditions for A and B to be strongly cosubnormal in <A,B> and, if Z is the hypercentre of G=<A,B>, we show that A and B are strongly cosubnormal if and only if G/Z is the direct product of AZ/Z and BZ/Z. We also show that projectors and residuals for certain formations can easily be constructed in such a group. Two subgroups A and B of a group G are N-connected if every cyclic subgroup of A is cosubnormal with every cyclic subgroup of B (N denotes the class of nilpotent groups). Though the concepts of strong cosubnormality and N-connectedness are clearly closely related, we give an example to show that they are not equivalent. We note, however, that if G is the product of the N-connected subgroups A and B, then A and B are strongly cosubnormal.
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Subjects:
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Finite group
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Hypercentre
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Strongly cosubnormal subgroups
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Subnormal subgroup
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Nilpotent group
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N-connected subgroups
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Formation
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Copyrigths:
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Reconocimiento - No comercial - Sin obra derivada (by-nc-nd)
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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/S0021-8693(02)00535-5
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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/S0021-8693(02)00535-5
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Project ID:
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info:eu-repo/grantAgreement/MEC//BFM2001-1667-C03-03/ES/Los grupos a través de sus acciones III/
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Description:
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This paper has been published in Journal of Algebra, 259(1):226-234 (2003).
Copyright 2003 by Elsevier.
http://dx.doi.org/10.1016/S0021-8693(02)00535-5
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Thanks:
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The first and the third authors have been supported by Proyecto BFM2001-1667-C03-03 from Ministerio de Ciencia y Tecnolog´ıa, Spain.
The third author has been supported by a grant from the Program of Support of Research ...[+]
The first and the third authors have been supported by Proyecto BFM2001-1667-C03-03 from Ministerio de Ciencia y Tecnolog´ıa, Spain.
The third author has been supported by a grant from the Program of Support of Research (Stays of Researchers in other academic institutions) of the Universitat Polit`ecnica de Val`encia.
Part of this research has been carried out during a visit of the third author to the School of Mathematical Sciences of the Australian National University in Canberra (Australia), to whom he wants to express his gratitude for their kindness and financial support.
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Type:
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Artículo
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