c-sections of maximal subgroups of finite groups

Let G be a finite group and let M be a maximal subgroup of G. Let K/L be a chief factor of G such that L less than or equal to M and G = MK. We call the group M boolean AND K/L a c-section of M in G. All c-sections of M are isomorphic. Using the concept of c-sections, we obtain some new characterizations of solvable and pi-solvable groups. (C) 2000 Academic Press.