Geodesic
On the influence of the fitting subgroup on the products of finite soluble groups
Problemy fiziki, matematiki i tehniki, no. 4 (2015), pp. 59-63

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A subgroup $H$ of a group $G$ is called $\mathrm{F}(G)$-subnormal if it is subnormal in $H\mathrm{F}(G)$. In the paper all closed under taking Schmidt subgroups saturated formations $\mathfrak{F}$ of finite soluble groups such that $\mathfrak{F}$ contains every soluble group $G$ which is the product of its $\mathrm{F}(G)$-subnormal $\mathfrak{F}$-subgroups were described. It was shown that a group $G$ which contains three supersoluble $\mathrm{F}(G)$-subnormal subgroups of pairwise coprime indexes in $G$ is supersoluble.
Keywords: the Fitting subgroup, $\mathrm{F}(G)$-subnormal subgroup, supersoluble group, saturated formation
Mots-clés : $\mathrm{F}(G)$-radical formation. 
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     author = {A. F. Vasil'ev and V. I. Murashka},
     title = {On the influence of the fitting subgroup on the products of finite soluble groups},
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     pages = {59--63},
     publisher = {mathdoc},
     number = {4},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2015_4_a10/}
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A. F. Vasil'ev; V. I. Murashka. On the influence of the fitting subgroup on the products of finite soluble groups. Problemy fiziki, matematiki i tehniki, no. 4 (2015), pp. 59-63. http://geodesic.mathdoc.fr/item/PFMT_2015_4_a10/