Group actions related to non-vanishing elements

‎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)‎.

کلیدواژه ها:

Finite ، Groups ، Fitting ، subgroup