  We prove that every finitely generated, virtually solvable minimax group can
be expressed as a homomorphic image of a virtually torsion-free, virtually
solvable minimax group. This result enables us to generalize a theorem of Ch.
Pittet and L. Saloff-Coste about random walks on finitely generated, virtually
solvable minimax groups. Moreover, the paper identifies properties, such as the
derived length and the nilpotency class of the Fitting subgroup, that are
preserved in the covering process. Finally, we determine exactly which
infinitely generated, virtually solvable minimax groups also possess this type
of cover.
