Group actions related to non-vanishing elements

Author(s):

Thomas Wolf

Abstract:
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).
Keywords:

Finite , groups , Fitting , subgroup

Language:
English
Published:
International Journal of Group Theory, Volume:3 Issue: 2, June 2014
Pages:
41 to 51
https://www.magiran.com/p1208271