Let $ \pi $ be a set of primes.A group $ G $ is said to be $ \pi $ -potent if, given an element $ a\in G $ and a positive integer $ \pi $ -number $ n $ dividing the order of $ a $ , there exists a homomorphism from $ G $ onto a finite group that maps $ a $ to an element of order $ n $ .It is proved that if $ G $ is a finitely generated metabelian group (or a residually finite abelian group, or a residually finite nilpotent group of finite rank, or a residually finite metabelian FATR group), then the following statements are equivalent for $ G $ :(1) $ G $ is $ \pi $ -potent;(2) $ G $ has no $ p $ -radicable elements of infinite order for any $ p\in\pi $ ;(3) $ G $ is virtually $ \pi $ -potent.It is also proved that if $ G $ is a residually finite soluble FATR group (or a finitely generated abelian-by-polycyclic group), then conditions (2) and (3) are equivalent for $ G $ .
