Geodesic
Finite groups with $\mathbb{P}$-subnormal biprimary subgroups
Trudy Instituta matematiki, Tome 21 (2013) no. 1, pp. 63-68

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In this paper we study finite groups with $\mathbb{P}$-subnormal biprimary dispersive subgroups. We prove that a group all of whose biprimary $p$-closed $pd$-subgroups are $\mathbb{P}$-subnormal is $p$-solvable, where $p$ is the largest prime divisor of the order of the group. We also prove that a group with biprimary $2$-nilpotent $\mathbb{P}$-subnormal $2d$-subgroups is solvable. 
@article{TIMB_2013_21_1_a7,
     author = {V. N. Kniahina},
     title = {Finite groups with $\mathbb{P}$-subnormal biprimary subgroups},
     journal = {Trudy Instituta matematiki},
     pages = {63--68},
     publisher = {mathdoc},
     volume = {21},
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     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMB_2013_21_1_a7/}
}
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V. N. Kniahina. Finite groups with $\mathbb{P}$-subnormal biprimary subgroups. Trudy Instituta matematiki, Tome 21 (2013) no. 1, pp. 63-68. http://geodesic.mathdoc.fr/item/TIMB_2013_21_1_a7/