J. Aust. Math. Soc.  79 (2005), 243-255

Some new permutability properties of hypercentrally embedded subgroups of finite groups

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

Abstract

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 -normalizers, for a saturated formation . In the soluble universe, -normalizers can be described as intersection of some pronormal subgroups of the group.

Download the article in PDF format (size 101 Kb)

Australian Mathematical Publishing Association Inc. ©  Australian MS