Geodesic
One characterization of the Gasch\"{u}tz subgroup of a~finite soluble group
Fundamentalʹnaâ i prikladnaâ matematika, Tome 20 (2015) no. 6, pp. 65-75

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Let $H$ be an $\mathfrak{N}$-prefrattini subgroup of a soluble finite group $G$ and $\Delta(G)$ be its Gaschütz subgroup. In this paper, it is proved that there exist elements $x,y \in G$ such that the equality $H \cap H^x \cap H^y = \Delta (G)$ holds. 
@article{FPM_2015_20_6_a3,
     author = {S. F. Kamornikov},
     title = {One characterization of the {Gasch\"{u}tz} subgroup of a~finite soluble group},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {65--75},
     publisher = {mathdoc},
     volume = {20},
     number = {6},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2015_20_6_a3/}
}
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S. F. Kamornikov. One characterization of the Gasch\"{u}tz subgroup of a~finite soluble group. Fundamentalʹnaâ i prikladnaâ matematika, Tome 20 (2015) no. 6, pp. 65-75. http://geodesic.mathdoc.fr/item/FPM_2015_20_6_a3/