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Zeros of Monomial Brauer Characters

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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 = G′Op′ (G) be the smallest normal subgroup such that G/H is an abelian p′-group. Suppose that g ∈ G 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.

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Acknowledgement

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

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Authors and Affiliations

  1. School of Mathematical Sciences, Yangzhou University, Yangzhou 225002, Jiangsu, China

    Xiaoyou Chen

  2. College of Science, Henan University of Technology, Zhengzhou, 450001, China

    Xiaoyou Chen

  3. School of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China

    Gang Chen

Authors
  1. Xiaoyou Chen
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  2. Gang Chen
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Correspondence to Xiaoyou Chen.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11571129, 11771356), the Natural Key Fund of Education Department of Henan Province (No. 17A110004) and the Natural Funds of Henan Province (Nos. 182102410049, 162300410066).

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Chen, X., Chen, G. Zeros of Monomial Brauer Characters. Chin. Ann. Math. Ser. B 40, 213–216 (2019). https://doi.org/10.1007/s11401-019-0127-7

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  • DOI: https://doi.org/10.1007/s11401-019-0127-7

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