Geodesic
On core of $p$-prefrattini subgroup of a finite soluble group
Problemy fiziki, matematiki i tehniki, no. 2 (2018), pp. 46-50

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Let $p$ be a prime, and $H$ is a $p$-prefrattini subgroup of a finite soluble group $G$. In the paper it is proved that there exist elements $x, y, z\in G$ such that the equality $H\cap H^x\cap H^y\cap H^z=\Phi_p(G)$ holds.
Keywords: finite soluble group, p-prefrattini subgroup, core of subgroup, generalized Frattini subgroup. 
@article{PFMT_2018_2_a5,
     author = {S. F. Kamornikov},
     title = {On core of $p$-prefrattini subgroup of a finite soluble group},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {46--50},
     publisher = {mathdoc},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2018_2_a5/}
}
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S. F. Kamornikov. On core of $p$-prefrattini subgroup of a finite soluble group. Problemy fiziki, matematiki i tehniki, no. 2 (2018), pp. 46-50. http://geodesic.mathdoc.fr/item/PFMT_2018_2_a5/