假设群A经自同构互素地作用在G上.设χ是G的一个A-不变不可约特征标,π(G,A)表示Glauberman-Isaacs特征标对映.对于B A, T.R.Wolf曾猜想χπ(G,A)是χπ(G,B)C的一个不可约成份,此处C = CG(A).设G = N /\ H且( N , H ) = 1,假定H是A-不...假设群A经自同构互素地作用在G上.设χ是G的一个A-不变不可约特征标,π(G,A)表示Glauberman-Isaacs特征标对映.对于B A, T.R.Wolf曾猜想χπ(G,A)是χπ(G,B)C的一个不可约成份,此处C = CG(A).设G = N /\ H且( N , H ) = 1,假定H是A-不变的且N是一个Sylow塔群, N的Sylow-子群是交换的.在本文中,我们证明了:如果这个猜想对所有H的A-不变子群成立,则猜想对G也成立.展开更多
A subgroup H of a finite 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, ｜...A subgroup H of a finite 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, we investigate the influence of s-semipermutablity of some subgroups of prime power order of a finite group on its supersolvablility.展开更多
文摘假设群A经自同构互素地作用在G上.设χ是G的一个A-不变不可约特征标,π(G,A)表示Glauberman-Isaacs特征标对映.对于B A, T.R.Wolf曾猜想χπ(G,A)是χπ(G,B)C的一个不可约成份,此处C = CG(A).设G = N /\ H且( N , H ) = 1,假定H是A-不变的且N是一个Sylow塔群, N的Sylow-子群是交换的.在本文中,我们证明了:如果这个猜想对所有H的A-不变子群成立,则猜想对G也成立.
基金NNSF of China (10471085)NSF of Shanxi Province of China (20011004)Key Proj. of Ministry of Education(02023)the Returned Overseas Students Foundation of Shanxi Province of China ([2004]7)
文摘A subgroup H of a finite 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, we investigate the influence of s-semipermutablity of some subgroups of prime power order of a finite group on its supersolvablility.
