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

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 \( \mathbb{X} \) .


Normal Subgroup Finite Group Simple Group Minimal Normal Subgroup Minimal Order 
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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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