Separability Properties of Nilpotent $\mathbb{Q}[x]$-Powered Groups II

In this paper, we study nilpotent $\mathbb{Q}$$[x]$-powered groups that satisfy the following property: For some set of primes $\omega$ in $\mathbb{Q}$$[x]$, every ${\omega }^{\mathrm{\prime }}$-isolated $\mathbb{Q}$$[x]$-subgroup in some family of its $\mathbb{Q}$$[x]$-subgroups is finite $\omega$-type separable.