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Some new permutability properties of hypercentrally embedded subgroups of finite groups

Part of: Structure and classification of infinite or finite groups Representation theory of groups

Published online by Cambridge University Press:  09 April 2009

L. M. Ezquerro  and
X. Soler-Escrivà
L. M. Ezquerro
Affiliation:
Departamento de Matemática e Informática, Universidad Pública de Navarra, Campus de Arrosadía, 31006 Pamplona, Spain, e-mail: ezquerro@unavarra.es
X. Soler-Escrivà
Affiliation:
Departament de Matemàtica Aplicada, Universitat d' Alacant, Campus de Sant Vicent, ap. Correus 99, 03080 Alacant, Spain, e-mail: xaro.soler@ua.es
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Abstract

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Hypercentrally embedded subgroups of finite groups can be characterized in terms of permutability as those subgroups which permute with all pronormal subgroups of the group. Despite that, in general, hypercentrally embedded subgroups do not permute with the intersection of pronormal subgroups, in this paper we prove that they permute with certain relevant types of subgroups which can be described as intersections of pronormal subgroups. We prove that hypercentrally embedded subgroups permute with subgroups of prefrattini type, which are intersections of maximal subgroups, and with F-normalizers, for a saturated formation F. In the soluble universe, F-normalizers can be described as intersection of some pronormal subgroups of the group.

Keywords

permutabilityfactorizations.

MSC classification

Secondary: 20D20: Sylow subgroups, Sylow properties, $pi$-groups, $pi$-structure 20D30: Series and lattices of subgroups 20E15: Chains and lattices of subgroups, subnormal subgroups 20D35: Subnormal subgroups 20D40: Products of subgroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 79 , Issue 2 , October 2005 , pp. 243 - 255
Copyright
Copyright © Australian Mathematical Society 2005

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