Group actions related to non-vanishing elements
نویسندگان
1 AG Algebra, Mathematisches Institut, Justus-Liebig-Universität Gießen, Arndtstrasse 2 35392, Giessen, Germany
2 Department of Mathematics, University of Kharazmi, P.O.Box 15614, Tehran, Iran
doi
10.22108/ijgt.2014.3669چکیده
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 $F(G)$.
