Geodesic
Fitting Classes with Given Properties of Hall Subgroups
Matematičeskie zametki, Tome 78 (2005) no. 2, pp. 234-240 
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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     author = {V. N. Zagurskii and N. T. Vorob'ev},
     title = {Fitting {Classes} with {Given} {Properties} of {Hall} {Subgroups}},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_78_2_a7/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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