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

Abstract

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 $\omega '$-isolated $\mathbb{Q}$$[x]$-subgroup in some family of its $\mathbb{Q}$$[x]$-subgroups is finite $\omega$-type separable.