A note on weakly σ-n-embedded subgroups of σ-full groups.

Autor: Hussain, Muhammad Tanveer, Zafar, Zain Ul Abadin, Ullah, Shamsher
Zdroj: Ricerche di Matematica; Nov2024, Vol. 73 Issue 5, p2801-2811, 11p
Abstrakt: Let σ = { σ i : i ∈ I } be a partition of the set P of all prime numbers. A subgroup H of a finite group G is called σ -subnormal in G if there is a chain of subgroups H = H 0 ⊆ H 1 ⊆ ⋯ ⊆ H n = G where, for every i = 1 , ... , n , H i - 1 normal in H i or H i / (H i - 1) H i is a σ i -group for some i ∈ I . A subgroup H of G is said to be weakly σ -n-embedded in G, if there is a σ -subnormal subgroup T of G such that H G = H T and H ∩ T ≤ H σ G , where the subgroup H σ G is generated by all σ -subnormal subgroups of G contained in H. In this paper, we study the properties of weakly σ -n-embedded subgroups and use them to determine the structure of finite groups. Some known results are gerneralized. [ABSTRACT FROM AUTHOR]
Databáze: Complementary Index
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