Permutable subnormal subgroups of finite groups
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Permutable subnormal subgroups of finite groups

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Permutable subnormal subgroups of finite groups

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Ballester-Bolinches, Adolfo Perfil; Beidleman, J.C.; Cossey, John; Esteban Romero, Ramón Perfil; Ragland, M.F.; Schmidt, Jack
Aquest document és un/a article, creat/da en: 2009
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 conjugate-permutability 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.

    Ballester Bolinches, Adolfo Beidleman, J.C. Cossey, John Esteban Romero, Ramón Ragland, M.F. Schmidt, Jack 2009 Permutable subnormal subgroups of finite groups Archiv der Mathematik 92 6 549 557
http://dx.doi.org/10.1007/s00013-009-2976-x
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