Geodesic
Formations and Products of $\mathrm F(G)$-Subnormal Subgroups of Finite Solvable Groups
Matematičeskie zametki, Tome 107 (2020) no. 3, pp. 376-390

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A subgroup $H$ of a finite group $G$ is said to be $\mathrm F(G)$-subnormal if it is subnormal in $H\mathrm F(G)$, where $\mathrm F(G)$ is the Fitting subgroup of $G$. In the paper, the problem of whether or not a formation $\mathfrak F$ contains products of $\mathrm F(G)$-subnormal $\mathfrak F$-subgroups of finite solvable groups is studied. In particular, solvable saturated formations $\mathfrak F$ with this property are described. Formation properties of groups having three solvable $\mathrm F(G)$-subnormal subgroups with pairwise coprime indices are studied. The supersolvability of any group $G$ having three supersolvable $\mathrm F(G)$-subnormal subgroups whose indices in $G$ are pairwise coprime is proved.
Keywords: finite group, nilpotent group, Fitting subgroup, saturated formation, Fitting formation.
Mots-clés : supersolvable group, solvable group 
@article{MZM_2020_107_3_a4,
     author = {A. F. Vasil'ev and V. I. Murashka},
     title = {Formations and {Products} of $\mathrm F(G)${-Subnormal} {Subgroups} of {Finite} {Solvable} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {376--390},
     publisher = {mathdoc},
     volume = {107},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_107_3_a4/}
}
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A. F. Vasil'ev; V. I. Murashka. Formations and Products of $\mathrm F(G)$-Subnormal Subgroups of Finite Solvable Groups. Matematičeskie zametki, Tome 107 (2020) no. 3, pp. 376-390. http://geodesic.mathdoc.fr/item/MZM_2020_107_3_a4/