Geodesic
$\Omega$-foliated formations and Fitting classes of finite groups
Diskretnaya Matematika, Tome 13 (2001) no. 3, pp. 125-144.

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A new functional approach to the study of classes of groups is proposed, resulting in description of all formations and Fitting classes of finite groups in the language of functions. The $\Omega$-foliated formations $\Omega F(f,\varphi)$ and $\Omega$-foliated Fitting classes $\Omega F(f,\varphi)$ with satellite $f$ and direction $\varphi$ are constructed. To each satellite $f$ there corresponds an infinite set of various directions $\varphi$. One direction leads to the previously considered $\Omega$-composite formations. In this way the $\Omega$-canonical and $\Omega$-free formations and Fitting classes are obtained. For a fixed direction $\varphi$ the structure of the minimal satellite $f$ is obtained. 
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V. A. Vedernikov; M. M. Sorokina. $\Omega$-foliated formations and Fitting classes of finite groups. Diskretnaya Matematika, Tome 13 (2001) no. 3, pp. 125-144. http://geodesic.mathdoc.fr/item/DM_2001_13_3_a8/

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