TY - JOUR
T1 - Zeros of Primitive Characters
AU - Wang , Wenyang
AU - Du , Ni
JO - Journal of Mathematical Study
VL - 1
SP - 67
EP - 70
PY - 2022
DA - 2022/01
SN - 55
DO - http://doi.org/10.4208/jms.v55n1.22.05
UR - https://global-sci.org/intro/article_detail/jms/20194.html
KW - Finite group, primitive character, vanishing element.
AB - <p style="text-align: justify;">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&nbsp; that&nbsp; if $g\in G$ and the order of $gG&#39;$ in the factor group $G/G&#39;$ does not divide $|{\rm Irr_{pri}}(G)|$, then there exists $\varphi \in {\rm Irr_{pri}}(G)$ such that $\varphi(g)=0$.</p>