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Chinese Annals of Mathematics, Series B

, Volume 40, Issue 2, pp 213–216 | Cite as

Zeros of Monomial Brauer Characters

  • Xiaoyou ChenEmail author
  • Gang Chen
Article
  • 14 Downloads

Abstract

Let G be a finite group and p be a fixed prime. A p-Brauer character of G is said to be monomial if it is induced from a linear p-Brauer character of some subgroup (not necessarily proper) of G. Denote by IBrm(G) the set of irreducible monomial p-Brauer characters of G. Let H = GOp (G) be the smallest normal subgroup such that G/H is an abelian p′-group. Suppose that gG is a p-regular element and the order of gH in the factor group G/H does not divide |IBrm(G)|. Then there exists φ ∈ IBrm(G) such that φ(g) = 0.

Keywords

Brauer character Finite group Vanishing regular element Monomial Brauer character 

2000 MR Subject Classification

20C15 20C20 

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Notes

Acknowledgement

The authors are very much thankful to the referees for their valuable suggestions and comments.

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Copyright information

© Fudan University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematical SciencesYangzhou UniversityJiangsuChina
  2. 2.College of ScienceHenan University of TechnologyZhengzhouChina
  3. 3.School of Mathematics and StatisticsCentral China Normal UniversityWuhanChina

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