A study on the structure of finite groups with $c$-subnormal subgroups

In this paper, we use the definition of the concept “c−Subnormal Subgroup” to study the structure of a given finite group G which contains some c−subnormal subgroups. We prove two main theorems, which answer the question of what conditions must hold so that G is an element in a formation U of supersoluble groups. Finally, we state many previous results which can be considered as special cases of these theorems.