有限群的半置换子群与s-半置换子群  

Semipermutable Subgroups and s-semipermutable Subgroups in Finite Groups

作　　者：李样明 LI Yangming(Department of Mathematics,Guangdong University of Education,Guangzhou,Guangdong,510310,P.R.China)

机构地区：[1]广东第二师范学院数学系,广州广东510310

出　　处：《数学进展》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)。

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.

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 

分 类 号：O152.2[理学—数学]