N-central group

Definition
Suppose $$G$$ is a group and $$n$$ is an integer other than 0. We say that $$G$$ is $$n$$-central if the exponent of the inner automorphism group of $$G$$ divides $$n$$.

Note that this is distinct from the notion of p-central group.

Facts

 * Frattini-in-center odd-order p-group implies p-power map is endomorphism
 * n-abelian implies n(n-1)-central