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

Abstract

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