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.

Voir la notice de l'article provenant de la source Math-Net.Ru

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/}
}
TY  - JOUR
AU  - S. F. Kamornikov
TI  - One characterization of the Gasch\"{u}tz subgroup of a~finite soluble group
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2015
SP  - 65
EP  - 75
VL  - 20
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2015_20_6_a3/
LA  - ru
ID  - FPM_2015_20_6_a3
ER  - 
%0 Journal Article
%A S. F. Kamornikov
%T One characterization of the Gasch\"{u}tz subgroup of a~finite soluble group
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2015
%P 65-75
%V 20
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2015_20_6_a3/
%G ru
%F FPM_2015_20_6_a3
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/

[1] Zenkov V. I., “Peresecheniya nilpotentnykh podgrupp v konechnykh gruppakh”, Fundament. i prikl. matem., 2:1 (1996), 1–92 | MR | Zbl

[2] Kamornikov S. F., Shemetkov L. A., “O normalizatore gashyutsevoi sistemy konechnoi razreshimoe gruppy”, Fundament. i prikl. matem., 14:8 (2008), 129–136

[3] Shemetkov L. A., Formatsii konechnykh grupp, Nauka, M., 1978 | MR

[4] Doerk K., Hawkes T., Finite Soluble Groups, Walter de Gruyter, Berlin, 1992 | MR

[5] Dolfi S., “Intersections of odd order Hall subgroups”, Bull. London Math. Soc., 37:1 (2005), 61–66 | DOI | MR | Zbl

[6] Dolfi S., “Large orbits in coprime actions of solvable groups”, Trans. Amer. Math. Soc., 360:1 (2008), 135–152 | DOI | MR | Zbl

[7] Gaschütz W., “Über die $\Phi$-Untergruppen endlicher Gruppen”, Math. Z., 58 (1953), 160–170 | DOI | MR | Zbl

[8] Gaschütz W., “Praefrattinigruppen”, Arch. Math., 13:3 (1962), 418–426 | DOI | MR | Zbl

[9] Hawkes T. O., “Analogues of prefrattini subgroups”, Proc. Int. Conf. Theory of Groups (Australian Nat. Univ., Canberra, 1965), Gordon and Breach, New York, 1967, 145–150 | MR

[10] Passman D. S., “Groups with normal solvable Hall $p'$-subgroups”, Trans. Amer. Math. Soc., 123:1 (1966), 99–111 | MR | Zbl

[11] Vdovin E. P., “Regular orbits of solvable linear $p'$-groups”, Sib. Electron. Math. Rep., 4 (2007), 345–360 | MR | Zbl