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Ukrainian Mathematical Journal

, Volume 66, Issue 10, pp 1603–1608 | Cite as

Factorizations of Finite Groups into r-Soluble Subgroups with Given Embeddings

  • V. N. Tyutyanov
  • V. N. Knyagina
Article
  • 30 Downloads

Let \( \mathbb{X} \) be a subset of the set of positive integers. A subgroup H of a group G is called \( \mathbb{X} \)-subnormal in G if there exists a chain of subgroups H = H 0H 1H n = G such that |H i : H i-1| ∈ \( \mathbb{X} \) for all i . We study the solubility and r -solubility of a finite group G = AB with some restrictions imposed on the subgroups A and B and on the set \( \mathbb{X} \) .

Keywords

Normal Subgroup Finite Group Simple Group Minimal Normal Subgroup Minimal Order 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • V. N. Tyutyanov
    • 1
  • V. N. Knyagina
    • 2
  1. 1.Gomel’ Branch of the “MITSO” International UniversityGomel’Belarus
  2. 2.State Institution of the “Gomel’ Engineering Institute,” Belarus Ministry of Emergency SituationsGomel’Belarus

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