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A question in the theory of saturated formations of finite soluble groups
Authors:A Ballester-Bolinches  K Doerk  L M Ezquerro
Institution:1. Departament d'àlgebra, Universitat de València, C/Dr. Moliner 50, 46100, Burjassot (València), Spain
2. Fachbereich Mathematik der Universit?t Mainz, Saarstr. 21, D-6500, Mainz, Germany
3. Departamento de Matemática e Informática, Universidad Pública de Navarra, Campus de Arrosadía, 31006, Pamplona, Spain
Abstract:This paper examines the following question. If 
$$\mathcal{H}$$
and 
$$\mathcal{F}$$
are saturated formations then 
$$\mathcal{H}_\mathcal{F} $$
is defined to be the class of all soluble groups whose 
$$\mathcal{H} - normalizers$$
belong to 
$$\mathcal{F}$$
. In general 
$$\mathcal{H}_\mathcal{F} $$
is a formation, but need not be a saturated formation. Here the smallest saturated formation containing 
$$\mathcal{H}_\mathcal{F} $$
is studied.
Keywords:
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