University of IsfahanInternational Journal of Group Theory2251-76503220140601Group actions related to non-vanishing elements4151366910.22108/ijgt.2014.3669ENThomasWolfOhio UniversityJournal Article20130904We characterize those groups $G$ and vector spaces $V$ such that $V$ is a faithful irreducible $G$-module and such that each $v$ in $V$ is centralized by a $G$-conjugate of a fixed non-identity element of the Fitting subgroup $F(G)$ of $G$. We also determine those $V$ and $G$ for which $V$ is a faithful quasi-primitive $G$-module and $F(G)$ has no regular orbit. We do use these to show in some cases that a non-vanishing element lies in $F(G)$.https://ijgt.ui.ac.ir/article_3669_cb1c4398181ca2cb64256d56ddd3c56c.pdf