Formations and Products of F(G)-Subnormal Subgroups of Finite Solvable Groups

A subgroup H of a finite group G is said to be F( G )- subnormal if it is subnormal in H F( 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,...

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Bibliographic Details
Published in:Mathematical Notes 2020-03, Vol.107 (3-4), p.413-424
Main Authors: Vasil’ev, A. F., Murashka, V. I.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Subgroups
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Summary:A subgroup H of a finite group G is said to be F( G )- subnormal if it is subnormal in H F( 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.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434620030050