Geodesic
On~$\mathrm K$-$\mathbb P$-Subnormal Subgroups of Finite Groups
Matematičeskie zametki, Tome 95 (2014) no. 4, pp. 517-528

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A subgroup $H$ of a group $G$ is said to be $\mathrm K$-$\mathbb P$-subnormal in $G$ if $H$ can be joined to the group by a chain of subgroups each of which is either normal in the next subgroup or of prime index in it. Properties of $\mathrm K$-$\mathbb P$-subnormal subgroups are obtained. A class of finite groups whose Sylow $p$-subgroups are $\mathrm K$-$\mathbb P$-subnormal in $G$ for every $p$ in a given set of primes is studied. Some products of $\mathrm K$-$\mathbb P$-subnormal subgroups are investigated.
Keywords: finite group, Sylow $p$-subgroup, $\mathrm K$-$\mathbb P$-subnormal subgroup, normal subgroup, subgroup of prime index, formation of groups.
Mots-clés : supersolvable group 
@article{MZM_2014_95_4_a3,
     author = {A. F. Vasil'ev and T. I. Vasilyeva and V. N. Tyutyanov},
     title = {On~$\mathrm K$-$\mathbb P${-Subnormal} {Subgroups} of {Finite} {Groups}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {517--528},
     publisher = {mathdoc},
     volume = {95},
     number = {4},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_95_4_a3/}
}
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A. F. Vasil'ev; T. I. Vasilyeva; V. N. Tyutyanov. On~$\mathrm K$-$\mathbb P$-Subnormal Subgroups of Finite Groups. Matematičeskie zametki, Tome 95 (2014) no. 4, pp. 517-528. http://geodesic.mathdoc.fr/item/MZM_2014_95_4_a3/