On σ-semipermutable subgroups of finite groups

2016/09/28 by Wenbin Guo, Guo, Wenbin, Alexander N. Skiba +1
Computer Science · Engineering · Mathematics · #20D10 #20D15 #20D30 #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1609.08815

openalex publication_date 2016/09/28 · openalex created_date 2016/10/07 · openalex updated_date 2026/07/28

Abstract

Let σ=\σ_i | i∈ I\ be some partition of the set of all primes ℙ, G a finite group and σ(G) =\σ_i |σ_i∩ π(G)≠ ∅ \. A set \cal H of subgroups of G is said to be a complete Hall σ-set of G if every member ≠ 1 of \cal H is a Hall σ_i-subgroup of G for some σ_i∈ σ and \cal H contains exact one Hall σ_i-subgroup of G for every σ_i∈ σ(G). A subgroup H of G is said to be: \emphσ-semipermutable in G with respect to \cal H if HH_i^x=H_i^xH for all x∈ G and all H_i∈ \cal H such that (|H|, |H_i|)=1; σ-semipermutable in G if H is σ-semipermutable in G with respect to some complete Hall σ-set of G. We study the structure of G being based on the assumption that some subgroups of G are σ-semipermutable in G.

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