A finite group is called a group, if every two cyclic subgroups of prime-power order are conjugate in . In other words is a group if is any prime divisor of and , where is a positive integer, then the action of , by conjugation, on the set of cyclic subgroups order is transitive. Some examples of groups are , In this thesis we study finite groups. We show that a homomorphic image of a group is again a group. Every nilpotent group is cyclic.
