University of Isfahan International Journal of Group Theory 2251-7650 3 2 2014 06 01 Group actions related to non-vanishing elements 41 51 3669 10.22108/ijgt.2014.3669 EN Thomas Wolf Ohio University Journal Article 2013 09 04 ‎We 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