Quelques propriétés sur la c-normalité des groupes

Abstract

In this thesis, we studied the c-normality of groups and its properties and the principal results established by Yanming Wang, which show that the notion of c-normality provides a characterization of the solvability of finite groups. The first main result states that a finite group is soluble if and only if all of its maximal subgroups are c-normal. The second result establishes a close relationship between the notion of c-normality and the normal index introduced by W. E. Deskins. More precisely, it proves that a maximal subgroup is c-normal if and only if its normal index is equal to its index in the group