特征标次数的商与有限群结构  

CHARACTER DEGREES QUOTIENTS AND STRUCTURES OF FINITE GROUPS

作　　者：钱国华[1] 

机构地区：[1]常熟理工学院数学系,江苏常熟215006

出　　处：《数学年刊（A辑）》2005年第3期307-312,共6页Chinese Annals of Mathematics

基　　金：江苏省高校自然科学研究计划资助的项目.

摘　　要：本文考察特征标次数的商如何影响有限群的结构.设G是非线性不可约特征标次数的商都是n次方自由的有限群,首先,对可解群G证明了它的导长能被一个仅依赖于n的函数所界定;其次,给出了当n≤3时有限群G的结构.The aim of this paper is to investigate how character degrees quotients of a finite group influence the structure of the group. Let G be a finite group whose non-linear irreducible character degrees quotients are all of nth-power-free. This paper obtains an upper bound of the derived length for solvable group G in terms of n, and shows the structure of the group when n≤3.

关 键 词：有限群 特征标 特征标次数的商 

分 类 号：O152.1[理学—数学]