On σ-Embedded and σ-n-Embedded Subgroups of Finite Groups


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Let G be a finite group, and let σ = {σi | iI} be a partition of the set of all primes ℙ and σ(G) = {σi | σiπ(G) ≠ ∅}. A set ℋ of subgroups of G is said to be a complete Hall σ-set of G if each nonidentity member of ℋ is a Hall σi-subgroup of G and ℋ has exactly one Hall σi-subgroup of G for every σiσ (G). A subgroup H of G is said to be σ-permutable in G if G possesses a complete Hall σ-set ℋ such that HAx = AxH for all A ∈ ℋ and xG. A subgroup H of G is said to be σ-n-embedded in G if there exists a normal subgroup T of G such that HT = HG and HTHσG, where HσG is the subgroup of H generated by all those subgroups of H that are σ-permutable in G. A subgroup H of G is said to be σ-embedded in G if there exists a σ-permutable subgroup T of G such that HT = HσG and HTHσG, where HσG is the intersection of all σ-permutable subgroups of G containing H. We study the structure of finite groups under the condition that some given subgroups of G are σ-embedded and σ-n-embedded. In particular, we give the conditions for a normal subgroup of G to be hypercyclically embedded.

Sobre autores

V. Amjid

School of Mathematical Sciences

Autor responsável pela correspondência
Email: venusamj@mail.ustc.edu.cn
República Popular da China, Hefei

W. Guo

School of Mathematical Sciences

Autor responsável pela correspondência
Email: wbguo@ustc.edu.cn
República Popular da China, Hefei

B. Li

College of Applied Mathematics

Autor responsável pela correspondência
Email: baojunli@cuit.edu.cn
República Popular da China, Chengdu

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