Some special classes of n-abelian groups

Document Type: Research Paper

Authors

1 Dipartimento di Matematica Università di Salerno - Italy

2 Dipartimento di Matematica, Università di Salerno - Italy

Abstract

‎‎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 $\mathfrak B_n\cap\mathfrak C_n$‎.

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