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M. M. Al-Shomrani, A. A. Heliel, and Adolfo Ballester-Bolinches.
On σ-subnormal closure.
Comm. Algebra, 48(8):3624–3627, 2020.
doi:10.1080/00927872.2020.1742348
Abstract
Let σ = {σi : i ∈ I} be a partition of the set ℙ of all prime numbers. A subgroup A of a finite group G is called σ–subnormal in G if there is chain of subgroups A = A0 ⊆ A1 ⊆⋯⊆ An = G with Aj-1 normal in Aj or Ai/CoreAi(Ai-1) is a σj-group for some j ∈ I, 1 ≤ i ≤ n. In this paper, the description of the unique smallest σ-subnormal subgroup of a σ-soluble group containing a given subgroup is obtained.
2020 Mathematics Subject Classification: 20D10, 20D20
Keywords: Finite group; σ-soluble group; σ-subnormal subgroup