Group actions related to non-vanishing elements

Thomas Wolf
2014 International Journal of Group Theory  
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).
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