A CHIEF FACTOR CHARACTERIZATION OF THE SOLVABLE RADICAL OF A FINITE GROUP

Let G be a finite group and let S(G) denote the solvable radical of G (the unique maximal subnormal solvable subgroup of G). In this article we present a chief factor characterization of S(G) that was suggested by the classic chief factor characterization of the Fitting subgroup of G (the unique maximal subnormal nilpotent subgroup of G). We close by extending these two results to a proper normal subgroup of G.