University of Isfahan International Journal of Group Theory 2251-7650 1 2 2012 06 01 Some special classes of n-Aabelian groups 19 24 474 10.22108/ijgt.2012.474 EN Costantino Delizia Dipartimento di Matematica Università di Salerno - Italy Antonio Tortora Dipartimento di Matematica, Università di Salerno - Italy Journal Article 2011 09 20 ‎‎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 $\mathfrak B_n\cap\mathfrak C_n$‎. https://ijgt.ui.ac.ir/article_474_8c61e9cf538261805804cae1cfb096f9.pdf