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On the characterization of the core of a \(\pi\)-prefrattini subgroup of a finite soluble group. (English. Russian original) Zbl 07079959
Sib. Math. J. 60, No. 1, 56-61 (2019); translation from Sib. Mat. Zh. 60, No. 1, 74-81 (2019).
Summary: 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 \(H\cap H^x \cap H^y \cap H^z = \Phi_\pi(G)\).
MSC:
20-XX Group theory and generalizations
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