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On \( {\varSigma}_t^{\sigma } \) -Closed Classes of Finite Groups

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Ukrainian Mathematical Journal Aims and scope

All analyzed groups are finite. Let σ = {σi| i ∈ I} be a partition of the set of all primes ℙ. If n is an integer, then the symbol σ(n) denotes a set {σi| σi ∩ π(n) ≠ ∅}. The integers n and m are called σ -coprime if σ(n) ∩ σ(m) =  ∅ . Let t > 1 be a natural number and let 𝔉 be a class of groups. Then we say that 𝔉 is \( {\varSigma}_t^{\sigma } \) -closed provided that 𝔉 contains each group G with subgroups A1, . . . , At 𝜖 𝔉 whose indices ∣G : A1 ∣ , …, ∣ G : At∣ are pairwise σ -coprime. We study \( {\varSigma}_t^{\sigma } \) -closed classes of finite groups.

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Authors and Affiliations

  1. University of Science and Technology of China, Hefei, China

    Ch. Zhang

  2. Skorina Gomel State University, Gomel, Belarus

    A. N. Skiba

Authors
  1. Ch. Zhang
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  2. A. N. Skiba
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, No. 12, pp. 1707–1716, December, 2018.

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Zhang, C., Skiba, A.N. On \( {\varSigma}_t^{\sigma } \) -Closed Classes of Finite Groups. Ukr Math J 70, 1966–1977 (2019). https://doi.org/10.1007/s11253-019-01619-6

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  • DOI: https://doi.org/10.1007/s11253-019-01619-6

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