A note on p-solvable and solvable finite groups - R. Khazal; N. P. Mukherjee (International Journal of Mathematics and Mathematical Sciences)
The notion of normal index is utilized in proving necessary and sufficient conditions for a group G to be respectively, p-solvable and solvable where p is the largest prime divisor of |G|. These are used further in identifying the largest normal p-solvable and normal solvable subgroups, respectively, of G.