NS^*-置换子群对有限群结构的影响  

Influence of NS^*-permutable Subgroups on the Structure of Finite Groups

作　　者：吴湘华 钟祥贵 WU Xianghua;ZHONG Xianggui(College of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541006, China)

机构地区：[1]广西师范大学数学与统计学院,广西桂林541006

出　　处：《广西师范大学学报（自然科学版）》2020年第5期42-47,共6页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金(11261007);广西自然科学基金(2014GXNSFAA118009)。

摘　　要：设G是有限群。子群H称为G的几乎S-置换子群,如果H≤K≤G,且对满足gcd(p,|H|)=1的任意素因子p,NK(H)包含K的某些Sylow p-子群;子群H称为G的NS^*-置换子群,如果存在G的正规子群T,使得HT■G,π(G/T)■π(H),且H∩T是G的几乎S-置换子群。本文应用G的某些素数幂阶NS^*-置换子群来刻画有限群的p-幂零性及超可解性,推广了相关文献的一些结果。Let G be a finite group.A subgroup H of G is called nearly S-permutable in G if for every prime p with gcd(p,|H|)=1 and for every subgroup K of G containing H the normalizer NK(H)contains some Sylow p-subgroup of K.A subgroup H of G is said to be NS^*-permutable subgroup of G if there exists a normal subgroup T of G such that HT■G,π(G/T)■π(H)and H∩T is nearly S-permutable subgroup of G.This article investigates the structure of G under the assumption that subgroups of prime power order are NS^*-permutable subgroups of G.Some recent results are generalized.

关 键 词：NS^*-置换子群 P-幂零群 超可解群 

分 类 号：O152.1[理学—数学]