Geodesic
Factorizations of One-Generated Composition Formations
Algebra i logika, Tome 40 (2001) no. 5, pp. 545-560.

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A non-empty formation $\mathfrak F$ of finite groups is said to be solubly saturated, or we call it a composition formation, if every finite group $G$ having a normal subgroup $N$ such that $G/\Phi(N)\in\mathfrak F$ belongs to $\mathfrak F$. An intersection of all composition formations containing a given group $G$ is denoted $c\operatorname{form}G$. Conditions are described under which $\mathfrak F=c\operatorname{form}G$ has the form $\mathfrak F=\mathfrak{MH}$, where $\mathfrak M\ne\mathfrak F\ne\mathfrak H$.
Keywords: composition formation (= solubly saturated formation of finite groups), solubly normal subgroup. 
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     author = {W. Guo and A. N. Skiba},
     title = {Factorizations of {One-Generated} {Composition} {Formations}},
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     number = {5},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2001_40_5_a3/}
}
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W. Guo; A. N. Skiba. Factorizations of One-Generated Composition Formations. Algebra i logika, Tome 40 (2001) no. 5, pp. 545-560. http://geodesic.mathdoc.fr/item/AL_2001_40_5_a3/