On the separability of subgroups of nilpotent groups by root classes of groups

Suppose that e is a class of groups consisting only of periodic groups and beta(e/0 is the set of prime numbers that do not divide the order of any element of a e-group. It is easy to see that if a subgroup Y of a group X is e-separable in this group, then it is beta(e/0-isolated in X. Let us say that X has the property e-Sep if all of its beta(e/0-isolated subgroups are r-separable. We find a condition that is sufficient for a nilpotent group N to have the property r-Sep providede is a root class. We also prove that if N is torsion-free, then the indicated condition is necessary for this group to have r-Sep.