数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (4): 1435-1440.doi: 10.1016/S0252-9602(12)60112-X

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ZEROS OF BRAUER CHARACTERS

王慧群1|陈晓友2|曾吉文3   

  1. 1.School of Mathematical Sciences, Xiamen University, Xiamen 361005, China|2.College of Science, Henan University of Technology, Zhengzhou 450001, China|3.School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
  • 收稿日期:2010-11-04 修回日期:2011-02-26 出版日期:2012-07-20 发布日期:2012-07-20
  • 基金资助:

    Chen research was supported by the Doctor Foundation of Henan University of Technology (2010BS048) and Tian Yuan Foundations (11126273, 11126271).

ZEROS OF BRAUER CHARACTERS

 WANG Hui-Qun1, CHEN Xiao-You2, ZENG Ji-Wen3   

  1. 1.School of Mathematical Sciences, Xiamen University, Xiamen 361005, China|2.College of Science, Henan University of Technology, Zhengzhou 450001, China|3.School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
  • Received:2010-11-04 Revised:2011-02-26 Online:2012-07-20 Published:2012-07-20
  • Supported by:

    Chen research was supported by the Doctor Foundation of Henan University of Technology (2010BS048) and Tian Yuan Foundations (11126273, 11126271).

摘要:

The authors obtain a sufficient condition to determine whether an element is a vanishing regular element of some Brauer character. More precisely, let G be a finite group and p be a fixed prime, and H = G'Op' (G); if g ∈ G0H0 with o(gH) coprime to the number of irreducible p-Brauer characters of G, then there always exists a nonlinear irreducible p-Brauer character which vanishes on g. The authors also show in this note that the sums of certain irreducible p-Brauer characters take the value zero on every element of G0H0.

关键词: vanishing regular element, Brauer character

Abstract:

The authors obtain a sufficient condition to determine whether an element is a vanishing regular element of some Brauer character. More precisely, let G be a finite group and p be a fixed prime, and H = G'Op' (G); if g ∈ G0H0 with o(gH) coprime to the number of irreducible p-Brauer characters of G, then there always exists a nonlinear irreducible p-Brauer character which vanishes on g. The authors also show in this note that the sums of certain irreducible p-Brauer characters take the value zero on every element of G0H0.

Key words: vanishing regular element, Brauer character

中图分类号: 

  • 20C15