On a Class of Generalized Nilpotent Groups,

We explore the class of generalized nilpotent groups in the universe c[formula] of all radical locally finite groups satisfying min- p for every prime p. We obtain that this class is the natural generalization of the class of finite nilpotent groups from the finite universe to the universe c[formula]. Moreover, the structure of -groups is determined explicitly. It is also shown that is a subgroup-closed c[formula]-formation and that in every c[formula]-group the Fitting subgroup is the unique maximal normal -subgroup.