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Sibirskii Matematicheskii Zhurnal, 2019, Volume 60, Number 1, Pages 74–81
DOI: https://doi.org/10.33048/smzh.2019.60.106 (Mi smj3059) 		 
On the characterization of the core of a $\pi$-prefrattini subgroup of a finite soluble group

X. Yia, S. F. Kamornikovb, L. Xiaoa

a Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, P.R. China
b F. Skorina Gomel State University, Gomel, Belarus
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DOI: https://doi.org/10.33048/smzh.2019.60.106
Abstract: Let $\pi$ be a set of primes and let $H$ be a $\pi$-prefrattini subgroup of a finite soluble group $G$. We prove that there exist elements $x, y, z\in G$ such that $H\cap H^x\cap H^y\cap H^z=\Phi_\pi(G)$.
Keywords: finite group, soluble group, $\pi$-prefrattini subgroup, Hall subgroup, Frattini subgroup.
Funding agency Grant number
National Natural Science Foundation of China 11471055
Zhejiang Provincial Natural Science Foundation of China LY18A010028
The first author was supported by the NNSF of China (Grant N 11471055) and the Zhejiang Provincial Natural Science Foundation of China (Grant N LY18A010028).
Received: 03.05.2018
Revised: 22.06.2018
Accepted: 17.08.2018
English version:
Siberian Mathematical Journal, 2019, Volume 60, Issue 1, Pages 56–61
DOI: https://doi.org/10.1134/S0037446619010063
Bibliographic databases:
Document Type: Article
UDC: 512.542
Language: Russian
Citation: X. Yi, S. F. Kamornikov, L. Xiao, “On the characterization of the core of a $\pi$-prefrattini subgroup of a finite soluble group”, Sibirsk. Mat. Zh., 60:1 (2019), 74–81; Siberian Math. J., 60:1 (2019), 56–61
Citation in format AMSBIB
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