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Kamornikov, Sergey. (1396). Intersections of prefrattini subgroups in finite soluble groups. , 6(2), 1-5. doi: 10.22108/ijgt.2017.11163
Sergey Kamornikov. "Intersections of prefrattini subgroups in finite soluble groups". , 6, 2, 1396, 1-5. doi: 10.22108/ijgt.2017.11163
Kamornikov, Sergey. (1396). 'Intersections of prefrattini subgroups in finite soluble groups', , 6(2), pp. 1-5. doi: 10.22108/ijgt.2017.11163
Kamornikov, Sergey. Intersections of prefrattini subgroups in finite soluble groups. , 1396; 6(2): 1-5. doi: 10.22108/ijgt.2017.11163

Intersections of prefrattini subgroups in finite soluble groups

International Journal of Group Theory
مقاله 1، دوره 6، شماره 2، شهریور 2017، صفحه 1-5    اصل مقاله (178.48 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2017.11163
نویسنده
Sergey Kamornikov*
Gomel Branch of International University MITSO
چکیده
‎Let $H$ be a prefrattini subgroup of a soluble finite group $G$‎. ‎In the‎ ‎paper it is proved that there exist elements $x,y \in G$ such that the equality‎ ‎$H \cap H^x \cap H^y = \Phi (G)$ holds‎.
کلیدواژه‌ها
‎finite soluble group‎؛ ‎Frattini subgroup‎؛ ‎prefrattini subgroup
مراجع
[1] K. Doerk and T. Hawkes, Finite soluble groups, de Gruyter Expositions in Mathematics, 4, Walter de Gruyter MGmbH & Co., Berlin, 1992.

[2] S. F. Kamornikov and L. A. Shemetkov, On the normalizer of a Gaschütz system of a finite soluble group, (Russian), translation in: J. Math. Sci., 166 (2010) 655–660.

[3] D. S. Passman, Groups with normal solvable Hall p′-subgroups, Trans. Amer. Math. Soc., 123 (1966) 99–111.

[4] V. I. Zenkov, Intersections of nilpotent subgroups in finite groups, (in Russian) Fundam. Prikl. Mat., 2 (1996) 1–92.

[5] S. Dolfi, Intersections of odd order Hall subgroups, Bull. London Math. Soc., 37 (2005) 61–66.

[6] S. Dolfi, Large orbits in coprime actions of solvable groups, Trans. Amer. Math. Soc., 360 (2008) 135–152.

[7] E. P. Vdovin, Regular orbits of solvable linear p′-groups, Sib. Elektron. Mat. Izv., 4 (2007) 345–360.

[8] V. D. Mazurov and E. I. Khukhro, Unsolved problems in group theory: The Kourovka Notebook, Russian Academy of Sciences, Siberian Branch, Institute of Mathematics, Novosibirsk, Russia, 2010.

[9] W. Gaschütz, Praefrattinigruppen, Arch. Math., 13 (1962) 418–426.

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