Year: 2022
Author: Wenyang Wang, Ni Du
Journal of Mathematical Study, Vol. 55 (2022), Iss. 1 : pp. 67–70
Abstract
Let $G$ be a finite group. An irreducible character $\chi$ of $G$ is said to be primitive if $\chi \neq \vartheta^{G}$ for any character $\vartheta$ of a proper subgroup of $G$. In this paper, we consider about the zeros of primitive characters. Denote by ${\rm Irr_{pri} }(G)$ the set of all irreducible primitive characters of $G$. We proved that if $g\in G$ and the order of $gG'$ in the factor group $G/G'$ does not divide $|{\rm Irr_{pri}}(G)|$, then there exists $\varphi \in {\rm Irr_{pri}}(G)$ such that $\varphi(g)=0$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v55n1.22.05
Journal of Mathematical Study, Vol. 55 (2022), Iss. 1 : pp. 67–70
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 4
Keywords: Finite group primitive character vanishing element.