  In recent years, the RFRS condition has been used to analyze virtual fibering
in 3-manifold topology. Agol's work shows that any 3-manifold with zero Euler
characteristic satisfying the RFRS condition on its fundamental group virtually
fibers over the circle. In this note we will show that a finitely generated
nilpotent group is either virtually abelian or is not virtually RFRS, a result
which may be of independent interest though not directly applicable to
3-manifold topology. As a corollary, we deduce that any RFRS group cannot
contain a nonabelian torsion-free nilpotent group. This result also illustrates
some of the interplay between residual torsion-free nilpotence and the RFRS
condition.
