Abstract
A subgroup H of a finite group G is said to be F(G)-subnormal if it is subnormal in HF(G), where F(G) is the Fitting subgroup of G. In the paper, the problem of whether or not a formation β contains products of F(G)-subnormal β-subgroups of finite solvable groups is studied. In particular, solvable saturated formations β with this property are described. Formation properties of groups having three solvable F(G)-subnormal subgroups with pairwise coprime indices are studied. The supersolvability of any group G having three supersolvable F(G)-subnormal subgroups whose indices in G are pairwise coprime is proved.
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Russian Text © The Author(s), 2020, published in Matematicheskie Zametki, 2020, Vol. 107, No. 3, pp. 376–390.
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Vasil’ev, A.F., Murashka, V.I. Formations and Products of F(G)-Subnormal Subgroups of Finite Solvable Groups. Math Notes 107, 413–424 (2020). https://doi.org/10.1134/S0001434620030050
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DOI: https://doi.org/10.1134/S0001434620030050