الخلاصة:
The first axis consists of two parts, the first containing the definitions and characteristics of FC-groups. The second part showing the relationship between this class, the class of PE-groups and the problem of P. Erdös. We also giving a solution to this problem developed by B. Neumann in [25], which allowed the extension of this problem and the introductions of the two classes and for certain classes of -groups.
The second axis includes two parts. The first is the basic elements in the theory of groups and some known classes of groups and their properties. The second part presents the findings of the researchers in their study
of the two categories and , for certain classes of -groups.
In the last axis we review the results that we have reached, which are :
- The study of the stability of the property FC by finite and torsion extensions.
- The study of some finitely generated groups belonging to the two classes and in those cases:
with special cases considered for k = 1 and k = 2.
