Geodesic
Critical $\Omega$-Fiber Formations of Finite Groups
Matematičeskie zametki, Tome 72 (2002) no. 2, pp. 269-282.

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Let $\mathfrak H$ be a class of finite groups. An $\Omega$-fiber formation $\mathfrak F$ of finite groups with direction $\varphi $ is said to be a minimal $\Omega$-fiber non-$\mathfrak H$-formation with direction $\varphi $, or briefly an $\mathfrak H_\Omega $-critical formation, if $\mathfrak F\nsubseteq \mathfrak H$, but any proper $\Omega$-fiber subformation with direction $\varphi $ in $\mathfrak F$ belongs to the class $\mathfrak H$. In the paper, a complete description of the structure of minimal $\Omega$-fiber non-$\mathfrak H$-formations of finite groups of two different directions is given. 
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M. M. Sorokina; N. V. Silenok. Critical $\Omega$-Fiber Formations of Finite Groups. Matematičeskie zametki, Tome 72 (2002) no. 2, pp. 269-282. http://geodesic.mathdoc.fr/item/MZM_2002_72_2_a10/

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