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 su...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.展开更多
A subgroup H of a group G is called semipermutable if it is permutable with every subgroup K of G with （｜H｜, ｜K｜） = 1, and s-semipermutable if it is permutable with every Sylow p-subgroup of G with （p, ｜H｜） ...A subgroup H of a group G is called semipermutable if it is permutable with every subgroup K of G with （｜H｜, ｜K｜） = 1, and s-semipermutable if it is permutable with every Sylow p-subgroup of G with （p, ｜H｜） = 1. In this paper, some sufficient conditions for a group to be solvable are obtained in terms of s-semipermutability.展开更多
基金supported in part by the project of NSF of China(12071092)the Science and Technology Program of Guangzhou Municipality,China(201804010088).
文摘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.
基金Supported by the NSF of China(10471085) Supported by the Shanxi Province(20051007) Supported by the Returned Chinese Students Found of Shanxi Province(Jinliuguanban [2004]7)
文摘A subgroup H of a group G is called semipermutable if it is permutable with every subgroup K of G with （｜H｜, ｜K｜） = 1, and s-semipermutable if it is permutable with every Sylow p-subgroup of G with （p, ｜H｜） = 1. In this paper, some sufficient conditions for a group to be solvable are obtained in terms of s-semipermutability.
