Geodesic
Remarks on the Supersolvability of a Group with Prime Indices of Some Subgroups
Matematičeskie zametki, Tome 107 (2020) no. 2, pp. 246-255

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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 $p\in\pi(G)$, there is a supersolvable subgroup of index $p$. New properties of groups containing two supersolvable subgroups of different prime indices are established.
Keywords: finite group, maximal subgroup, index of a subgroup.
Mots-clés : supersolvable group 
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     author = {V. S. Monakhov and A. A. Trofimuk},
     title = {Remarks on the {Supersolvability} of a {Group} with {Prime} {Indices} of {Some} {Subgroups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {246--255},
     publisher = {mathdoc},
     volume = {107},
     number = {2},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2020_107_2_a7/}
}
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V. S. Monakhov; A. A. Trofimuk. Remarks on the Supersolvability of a Group with Prime Indices of Some Subgroups. Matematičeskie zametki, Tome 107 (2020) no. 2, pp. 246-255. http://geodesic.mathdoc.fr/item/MZM_2020_107_2_a7/