Abstract
For an arbitrary partition \(\sigma\) of the set \(\mathbb{P}\) of all primes, a sufficient condition for the \(\sigma\)-subnormality of a subgroup in a finite group is given. It is proved that, if a complete Hall set of type \(\sigma\) is reduced into a subgroup \(H\) of a \(\sigma\)-complete finite group \(G\) all of whose non-Abelian composition factors are alternating groups, Suzuki groups, or Ree groups, then \(H\) is \(\sigma\)-subnormal in \(G\).
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Translated from Matematicheskie Zametki, 2021, Vol. 109, pp. 564-570 https://doi.org/10.4213/mzm12887.
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Kamornikov, S.F., Tyutyanov, V.N. On the Kegel–Wielandt \(\sigma\)-Problem. Math Notes 109, 580–584 (2021). https://doi.org/10.1134/S0001434621030263
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DOI: https://doi.org/10.1134/S0001434621030263