SOME SPECIAL CLASSES OF n-ABELIAN GROUPS

Abstract. Given an integer n, we denote by B_n and C_n the classes of all groups G for which the map n : g ؟ g^n is a monomorphism and an epimorphism of G, respectively. In this paper we give a characterization for groups in B_n and for groups in C_n. We also obtain an arithmetic description of the set of all integers n such that a group G is in B_n \ C_n.