Abstract
In the paper, a characterization is obtained for a finite group such that, for each prime p, every maximal subgroup of any Sylow p-subgroup of this group is contained in a subgroup of index p; in particular, such groups are supersolvable. It is proved that a group G is supersolvable if and only if, for every prime p ∈ π(G), there is a supersolvable subgroup of index p. New properties of groups containing two supersolvable subgroups of different prime indices are established.
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Russian Text © The Author(s), 2020, published in Matematicheskie Zametki, 2020, Vol. 107, No. 2, pp. 246–255.
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Monakhov, V.S., Trofimuk, A.A. Remarks on the Supersolvability of a Group with Prime Indices of Some Subgroups. Math Notes 107, 288–295 (2020). https://doi.org/10.1134/S0001434620010290
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DOI: https://doi.org/10.1134/S0001434620010290