极大类p群的非线性非忠实不可约特征标个数  

The number of nonlinear non-faithful irreducible character of p-group of maximal class

作　　者：王雪 李亚利[1] WANG Xue;LI Ya-li(School of Mathematics and Computer Science,Yunnan Minzu University,Kunming 650500,China)

机构地区：[1]云南民族大学数学与计算机科学学院,云南昆明650500

出　　处：《云南民族大学学报（自然科学版）》2024年第2期266-270,共5页Journal of Yunnan Minzu University:Natural Sciences Edition

基　　金：国家自然科学基金(12201553,11861078);云南民族大学教学研究项目(2022JG-032).

摘　　要：利用极大类p群的性质以及有限群的特征标理论探究了极大类p群G的非线性非忠实不可约特征标的个数.证明了p^(n)阶的极大类p群G的非线性非忠实不可约特征标的个数等于p^(n-1)阶的极大类p群G/Z(G)的非线性不可约特征标的个数.特别地,分析了只有3个非线性非忠实不可约特征标的有限p群的性质.In This paper,we studied the number of nonlinear non-faithful irreducible characters of p-group G of maximal class,by using the properties of p-group of maximal class and character theory of finite groups.It is proved that the number of nonlinear non-faithful irreducible characters of p-group G of maximal class of order p^(n)equal the number of nonlinear irreducible characters of p-group G/Z(G)of maximal class of order p^(n-1).In particular,the properties of finite groups with exactly three nonlinear non-faithful irreducible characters are analyzed.

关 键 词：极大类p群 非线性不可约特征标 非忠实不可约特征标 

分 类 号：O152[理学—数学]