Semipermutable subgroups and s-semipermutable subgroups in finite groups  

作　　者：Yangming LI 

机构地区：[1]School of Mathematics,Guangdong University of Education,Guangzhou 510310,China

出　　处：《Frontiers of Mathematics in China》2022年第1期23-46,共24页中国高等学校学术文摘·数学（英文）

基　　金：supported in part by the project of NSF of China(12071092);the Science and Technology Program of Guangzhou Municipality,China(201804010088).

摘　　要：Suppose that H is a subgroup of a finite group G.We call H is semipermutable in G if HK=KH iov any subgroup K of G such that(|H|,|K|)=1;H is s-semipermutable in G if HG_(p)=G_(p)H,for any Sylow p-subgroup G_(p)of G such that(|H|,p)=1.These two concepts have been received the attention of many scholars in group theory since they were introduced by Professor 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 gives some thoughts in the research process.

关 键 词：Semipermutable subgroup s-semipermutable subgroup maximal subgroup minimal subgroup the generalized Fitting-subgroup formation 

分 类 号：O152.1[理学—数学]