N-abelian group

Definition

Suppose $n$ is an integer. A group $G$ is termed a $n$-abelian group if the $n^{th}$ power map $x\mapsto x^n$ is an endomorphism of $G$, i.e., $(xy{)}^n=x^n{y}^n$ for all $x,y\in G$. If this is the case, then the $n^{th}$ power map is termed a universal power endomorphism of $G$.