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A Criterion for the \(\sigma\)-Subnormality of a Subgroup in a Finite \(3^{'}\)-Group

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Abstract

For any partition \(\sigma\) of the set \(\mathbb{P}\) of all primes, it is proved that if a subgroup H of a finite \(3^{'}\)-group G is \(\sigma\)-subnormal in \(<H,H^x>\) for any \(x \in G\), then H is \(\sigma\)-subnormal in G.

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Funding

The work by S.F. Kamornikov is conducted under financial support of the Ministry of Education of the Republic of Belarus (GR no. 20191056).

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Authors and Affiliations

  1. Francisk Skorina Gomel State University, 104 Sovetskaya str., 246019, Gomel, Republic of Belarus

    S. F. Kamornikov

  2. Gomel Branch of the International University «MITSO», 46 a October Ave., 246029, Gomel, Republic of 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 Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2020, No. 8, pp. 36–43.

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Kamornikov, S.F., Tyutyanov, V.N. A Criterion for the \(\sigma\)-Subnormality of a Subgroup in a Finite \(3^{'}\)-Group. Russ Math. 64, 30–36 (2020). https://doi.org/10.3103/S1066369X20080046

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  • DOI: https://doi.org/10.3103/S1066369X20080046

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