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

  • Ch. Zhang
  • A. N. Skiba
Article

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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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Ch. Zhang
    • 1
  • A. N. Skiba
    • 2
  1. 1.University of Science and Technology of ChinaHefeiChina
  2. 2.Skorina Gomel State UniversityGomelBelarus

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