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| Zeros of Monomial Brauer Characters |
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Citation： |
Xiaoyou CHEN,Gang CHEN.Zeros of Monomial Brauer Characters[J].Chinese Annals of Mathematics B,2019,40(2):213~216 |
| Page view： 1710
Net amount： 1780 |
Authors： |
Xiaoyou CHEN; Gang CHEN |
Foundation： |
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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| 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 ${\rm IBr}_{m}(G)$ the set of irreducible
monomial $p$-Brauer characters of $G$. Let $H=G'{\bf O}^{p'}(G)$ be
the smallest normal subgroup such that $G/H$ is an abelian
$p'$-group. Suppose that $g\in G$ is a $p$-regular element and the
order of $gH$ in the factor group $G/H$ does not divide $|{\rm
IBr}_{m}(G)|$. Then there exists $\varphi\in {\rm IBr}_{m}(G)$ such
that $\varphi(g)=0$. |
Keywords： |
Brauer character, Finite group, Vanishing regular element, Monomial Brauer character |
Classification： |
20C15, 20C20 |
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