On sigma-subnormal subgroups of factorised finite groups
| Autor: | S. F. Kamornikov, Adolfo Ballester-Bolinches, Xiaolan Yi, M. C. Pedraza-Aguilera |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Finite group
Algebra and Number Theory Soluble group 010102 general mathematics Prime number 01 natural sciences Combinatorics 0103 physical sciences Partition (number theory) 010307 mathematical physics 0101 mathematics Sigma-Subnormal subgroup Sigma-Nilpotency MATEMATICA APLICADA Factorised group Mathematics |
| Zdroj: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia instname |
| Popis: | Let σ = { σ i : i ∈ I } be a partition of the set P of all prime numbers. A subgroup X of a finite group G is called σ-subnormal in G if there is chain of subgroups X = X 0 ⊆ X 1 ⊆ ⋯ ⊆ X n = G with X i − 1 normal in X i or X i / C o r e X i ( X i − 1 ) is a σ i -group for some i ∈ I , 1 ≤ i ≤ n . In the special case that σ is the partition of P into sets containing exactly one prime each, the σ-subnormality reduces to the familiar case of subnormality. If a finite soluble group G = A B is factorised as the product of the subgroups A and B, and X is a subgroup of G such that X is σ-subnormal in 〈 X , X g 〉 for all g ∈ A ∪ B , we prove that X is σ-subnormal in G. This is an extension of a subnormality criteria due to Maier and Sidki and Casolo. |
| Databáze: | OpenAIRE |
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