Characterizations of minimal non-solvable Fitting p-groups

Abstract

Let G be a minimal non-solvable Fitting p-group. Our main results are that G has uncountbly many subgroups and that G has a homomorphic image G with a proper subgroup X such that CG(X) = 1. We also define the solvabilizer of a solvable group and consider the minimal non-solvability problem in another context. © Walter de Gruyter 2008.