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关于Glauberman-Isaacs特征标对映的注记
引用本文:何立国,何春艳. 关于Glauberman-Isaacs特征标对映的注记[J]. 数学研究, 2005, 38(3): 255-259
作者姓名:何立国  何春艳
作者单位:1. 哈尔滨工业大学数学系,哈尔滨,150001;沈阳工业大学数学系,沈阳,110023
2. 哈尔滨学院初教部,哈尔滨,150086
摘    要: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)a的一个不可约成份,此处C=CG(A).设G=N(X)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.

关 键 词:Glauberman-Isaacs特征标对映  群作用  群的半直积  Sylow塔群
修稿时间:2004-05-09

A Note on Glauberman-Isaacs Character Correspondences
He Liguo,He Chunyan. A Note on Glauberman-Isaacs Character Correspondences[J]. Journal of Mathematical Study, 2005, 38(3): 255-259
Authors:He Liguo  He Chunyan
Affiliation:He Liguo~1,2 He Chunyan~3
Abstract:Suppose that a group A acts on a group G of coprime order via automorphisms. Let χ be an A-invariant irreducible character of G and π(G, A ) denote the character correspondences. For B ≤A, T. R. Wolf once conjectured that χπ(G, A ) is an irreducible constituent of χπ(G, B )e, where C =CG (A). Let G=N (X) H be such that (|N|, |H|)= 1, suppose that H is A-invariant and N is a Sylow tower group and all of Sylow subgroups of N are abelian. In this note, we prove that if the Conjecture holds for all of A-invariant subgroups of H, then the Conjecture holds for G.
Keywords:Glauberman-Isaacs character correspondences  Group action  Semidirect product of groups  Sylow tower group
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