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 \mathfrak{U} of supersoluble groups. Finally, we state many previous results which can be considered as special cases of these theorems.

Keywords:

Saturated formation , c-subnormal subgroup , Sylow subgroup , supersoluble group