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
X. Soler-Escrivà
  Departament de Matemàtica Aplicada
  Universitat d'Alacant
  Campus de Sant Vicent
  ap. Correus 99
  03080 Alacant

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 ${\mathcal{F}}$-normalizers, for a saturated formation $\mathcal{F}$. In the soluble universe, $\mathcal{F}$-normalizers can be described as intersection of some pronormal subgroups of the group.
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