Geodesic
On hyperradical formations of finite groups
Trudy Instituta matematiki, Tome 16 (2008) no. 1, pp. 9-12

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A formation $\mathfrak F$ of finite groups is called a hyperradical formation if $\mathfrak F$ is a normally subgroup-closed formation and $\mathfrak F$ contains every group $G=\langle H,K\rangle$, where $H$ and $K$ are $\mathfrak F$-subnormal $\mathfrak F$-subgroups of $G$. It is proved that every subgroup-closed hyperradical formation of finite groups is a lattice solubly saturated Fitting formation. 
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A. F. Vasil'ev; I. N. Khalimonchik. On hyperradical formations of finite groups. Trudy Instituta matematiki, Tome 16 (2008) no. 1, pp. 9-12. http://geodesic.mathdoc.fr/item/TIMB_2008_16_1_a2/