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On σ-Subnormal Subgroups of Finite Groups

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Abstract

Let p be a prime and let σ = {{p}, {p}′} be a partition of the set ℙ of all primes. We prove the following conjecture by Skiba: If each complete Hall set of type σ in a finite group G is reducible to some subgroup H of G then H is σ-subnormal in G.

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Authors and Affiliations

  1. F. Skorina Gomel State University, Gomel, Belarus

    S. F. Kamornikov

  2. MITSO International University, Gomel, Belarus

    V. N. Tyutyanov

Authors
  1. S. F. Kamornikov
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  2. V. N. Tyutyanov
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Corresponding authors

Correspondence to S. F. Kamornikov or V. N. Tyutyanov.

Additional information

Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 2, pp. 337–343.

S. F. Kamornikov was supported by the Ministry of Education of the Republic of Belarus (Grant GR 20191056).

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Kamornikov, S.F., Tyutyanov, V.N. On σ-Subnormal Subgroups of Finite Groups. Sib Math J 61, 266–270 (2020). https://doi.org/10.1134/S0037446620020093

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  • DOI: https://doi.org/10.1134/S0037446620020093

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