Brauer特征标表的两个性质  

Two Properties of Brauer Character Tables

作　　者：陈晓友[1,2] 杜妮[1] 

机构地区：[1]厦门大学数学科学学院,福建厦门361005 [2]河南工业大学理学院

出　　处：《厦门大学学报（自然科学版）》2011年第3期495-497,共3页Journal of Xiamen University：Natural Science

摘　　要：为了利用有限群模表示理论去得到有限群中一些数量性质的刻画,运用Schur-Zassenhaus定理以及模表示理论,证明了任意素数p不整除任一个有限群的p-正则元的个数.根据Brauer特征标表,可以得到一些数论信息.运用模表示论和Galois理论给出了在任意有限群的Brauer特征标表中每行元素的和为有理整数.另外,如果一个有限群为p-可解群,则其Brauer特征标表的每列元素和为有理整数.The aim of this note is to characterize some quantitative properties in a finite group by using modular representation theory.Utilizing the Schur-Zassenhaus theorem and modular representation theory,the authors prove in this note that any prime p does not divide the number of p-regular elements of a finite group.According to the Brauer character table of a finite group,some information on number theory can be obtained.Using modular representation theory and Galois theory,the authors present in this note that every row sum in the Brauer character table of any finite group is a rational integer.In addition,if a finite group is p-solvable,then each column sum in its Brauer character table is a rational integer.

关 键 词：Brauer特征标表 BRAUER特征标 广义特征标 p-正则元 

分 类 号：O152[理学—数学]