On the Characterization of the Core of a  π -Prefrattini Subgroup of a Finite Soluble Group

X. Yi; S. F. Kamornikov; L. Xiao

doi:10.1134/S0037446619010063

On the Characterization of the Core of a π-Prefrattini Subgroup of a Finite Soluble Group

Authors: Yi X.¹, Kamornikov S.F.², Xiao L.¹
Affiliations:
1. Department of Mathematics
2. F. Skorina Gomel State University
Issue: Vol 60, No 1 (2019)
Pages: 56-61
Section: Article
URL: https://journals.rcsi.science/0037-4466/article/view/172179
DOI: https://doi.org/10.1134/S0037446619010063
ID: 172179

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Abstract

Let π be a set of primes and let H be a π-prefrattini subgroup of a finite soluble group G. We prove that there exist elements x, y, z ∈ G such that H ∩ H^x ∩ H^y ∩ H^z = Φ_π(G).