Geodesic
Fitting Classes with Given Properties of Hall Subgroups
Matematičeskie zametki, Tome 78 (2005) no. 2, pp. 234-240.

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In the theory of formations of finite solvable groups, there is a well-known result due to Blessenohl claiming that, for any local formation $\mathfrak F$, the class of groups for which every Hall $\pi$-subgroup belongs to $\mathfrak F$ also is a local formation. In the present paper, we obtain a result exactly dual to that indicated in the theory of Fitting classes. We prove that if a Fitting class $\mathfrak F$ is local, then the class of all groups all of whose Hall $\pi$-subgroups belong to $\mathfrak F$ is also local. 
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V. N. Zagurskii; N. T. Vorob'ev. Fitting Classes with Given Properties of Hall Subgroups. Matematičeskie zametki, Tome 78 (2005) no. 2, pp. 234-240. http://geodesic.mathdoc.fr/item/MZM_2005_78_2_a7/

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