摘要
设H为G的子群,称H在G中半置换,如果HK=KH对任意满足条件(|H|,|K|)=1的G的子群K都成立;称H在G中s-半置换,如果HP=PH对任意P∈Sylp(G)都成立,其中(|H|,p)=1.这两个概念自陈重穆1987年提出后,获得国内外许多学者的关注,应用此概念近几十年来有大量的文章出现.本文对这方面的成果进行总结,给出研究过程中的思路.
Suppose that H is a subgroup of a finite group G.We call H is semipermutable in G if HK=KH for any subgroup K of G such that(|H|,|K|)= 1;we call H is s-semipermutable in G if HG_p= G_pH,for any Sylow p-subgroup G_p of G such that(|H|,p)= 1.These two concepts have been received attention of many scholars in group theory since they were introduced by Zhongmu Chen in 1987.In recent decades,there are a lot of papers published via the application of these concepts.Here we summarize the results in this area and give some thoughts in the research process.
作者
李样明
LI Yangming(Department of Mathematics,Guangdong University of Education,Guangzhou,Guangdong,510310,P.R.China)
出处
《数学进展》
CSCD
北大核心
2020年第4期385-400,共16页
Advances in Mathematics（China）
基金
广东省基础研究及应用研究重大项目(自然科学)(No.2017KZDXM058)
广州市科技计划项目(No.201804010088)。
关键词
半置换子群
S-半置换子群
极大子群
极小子群
广义FITTING子群
群系
semipermutable subgroups
s-semipermutable subgroups
maximal subgroups
minimal subgroups
generalized Fitting-subgroup
formation
