Ballester Bolinches, A.; Beidleman, JC.; Cossey, J.; Esteban Romero, R.; Rangland, MF.; Schmidt, J. (2009). Permutable subnormal subgroups of finite groups. Archiv der Mathematik. 92(6):549-557. https://doi.org/10.1007/s00013-009-2976-x
Por favor, use este identificador para citar o enlazar este ítem: http://hdl.handle.net/10251/54873
Título:
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Permutable subnormal subgroups of finite groups
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Autor:
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Ballester Bolinches, Adolfo
Beidleman, J. C.
Cossey, John
Esteban Romero, Ramón
Rangland, M. F.
Schmidt, Jack
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Entidad UPV:
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Universitat Politècnica de València. Departamento de Matemática Aplicada - Departament de Matemàtica Aplicada
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Fecha difusión:
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Resumen:
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The aim of this paper is to prove certain characterization theorems
for groups in which permutability is a transitive relation, the so called
PT -groups. In particular, it is shown that the finite solvable PT -groups,
the ...[+]
The aim of this paper is to prove certain characterization theorems
for groups in which permutability is a transitive relation, the so called
PT -groups. In particular, it is shown that the finite solvable PT -groups,
the finite solvable groups in which every subnormal subgroup of defect two
is permutable, the finite solvable groups in which every normal subgroup
is permutable sensitive, and the finite solvable groups in which conjugatepermutability
and permutability coincide are all one and the same class. This
follows from our main result which says that the finite modular p-groups,
p a prime, are those p-groups in which every subnormal subgroup of defect
two is permutable or, equivalently, in which every normal subgroup is permutable
sensitive. However, there exist finite insolvable groups which are not
PT -groups but all subnormal subgroups of defect two are permutable.
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Palabras clave:
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Permutable
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Subnormal
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PT -group
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Conjugate-Permutable
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Modular p-group
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Derechos de uso:
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Reserva de todos los derechos
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Fuente:
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Archiv der Mathematik. (issn:
0003-889X
)
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DOI:
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10.1007/s00013-009-2976-x
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Editorial:
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Springer Verlag (Germany)
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Versión del editor:
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http://link.springer.com/article/10.1007%2Fs00013-009-2976-x
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Código del Proyecto:
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info:eu-repo/grantAgreement/MEC//MTM2007-68010-C03-02/ES/GRUPOS: ESTRUCTURA Y APLICACIONES II/
info:eu-repo/grantAgreement/GVA//GV%2F2007%2F243/
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Descripción:
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The final publication is available at Springer via http://dx.doi.org/10.1007/s00013-009-2976-x
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Agradecimientos:
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This paper was started and completed in two visits of the first author to the Department of Mathematics of the Australian National University, Canberra, Australia. He is grateful to the Department of Mathematics for its ...[+]
This paper was started and completed in two visits of the first author to the Department of Mathematics of the Australian National University, Canberra, Australia. He is grateful to the Department of Mathematics for its warm hospitality and financial support while this investigation was carried out. He also gratefully acknowledges financial support by Grant MTM2007-68010-C03-02 from MEC (Spanish Government) and FEDER. The research of the fourth author has been supported by the Grants MTM2007-68010-C03-02 from MEC (Spanish Government) and FEDER, and GV/2007/243 from Generalitat (Valencian Government). He thanks all these institutions for their financial support.
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Tipo:
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Artículo
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