Acta mathematica scientia, Series B >
ZEROS OF BRAUER CHARACTERS
Received date: 2010-11-04
Revised date: 2011-02-26
Online 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).
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 ∈ G0− H0 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 G0− H0.
Key words： vanishing regular element; Brauer character
WANG Hui-Qun , CHEN Xiao-You , ZENG Ji-Wen . ZEROS OF BRAUER CHARACTERS[J]. Acta mathematica scientia, Series B, 2012 , 32(4) : 1435 -1440 . DOI: 10.1016/S0252-9602(12)60112-X
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