On C-section and C-index of finite groups

Let G be a finite group and let M be a maximal subgroup of G. For each chief factor K/L of G such that L≤M and G=MK, we called the group M∩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 π-solvable groups, and generalize a number of known results on the normal index and c-normality.