  In this paper, we expand certain aspects of Nielsen periodic point theory
from tori and nilmanifolds to infra-nilmanifolds. We show that
infra-nilmanifolds are essentially reducible to the GCD and essentially toral.
With these structural properties in mind, we develop a method to compute the
full Nielsen-Jiang number $NF_n(f)$. We also determine for which maps it holds
that $NF_n(f)=N(f^n)$, for all $n$.
