On σ-semipermutable Subgroups of Finite Groups

作     者：Wen Bin GUO Alexander N. SKIBA 

作者机构：Department of Mathematics University of Science and Technology of China Hefei 230026 P. R. China Department of Mathematics and Technologies of ProgrammingFrancisk Skorina Gomel State University Gomel 246019 Belarus 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2018年第34卷第9期

页      面：1379-1390页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：Supported by NNSF(Grant No.11771409) Wu Wen-Tsun Key Laboratory of Mathematics of Chinese Academy of Sciences 

主　　题：Finite group Hall subgroup p-soluble group p-supersoluble group σ-semipermutable subgroup 

摘      要：Let a = {σi｜ i ∈ I} be some partition of the set of all primes P, G a finite group and σ（G） = {σi｜σi ∩ π （G） ≠ Ф}. A set H of subgroups of G is said to be a complete Hall or-set of G if every member ≠ 1 of H is a Hall σi-subgroup of G for some σi ∈ σ and H contains exactly one Hall σi-subgroup of G for every σi ∈ σ（G）. A subgroup H of G is said to be： σ-semipermutablc in G with respect to H if HHi x = Hi x H for all x ∈ G and all x ∈ G and all Hi ∈H such that （｜H｜, ｜Hi｜） = 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.