On chief factors of finite groups

Let H and K be normal subgroups of a finite group G and let K≤H. If A is a subgroup of G such that AH=AK or A∩H=A∩K, we say that A covers or avoids H/K respectively. The purpose of this paper is to investigate factor groups of a finite group G using this concept. We get some characterizations of a finite group being solvable or supersolvable and generalize some known results.