Some special classes of n-abelian groups

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

کلیدواژه ها:

n-abelian group ، abelian group ، finite exponent