  In this paper it is proven that if the group of covering translations of the
covering space of a compact, connected, $P^2$-irreducible 3-manifold
corresponding to a non-trivial, finitely-generated subgroup of its fundamental
group is infinite, then either the covering space is almost compact or the
subgroup is infinite cyclic and has normalizer a non-finitely-generated
subgroup of the rational numbers. In the first case additional information is
obtained which is then used to relate Thurston's hyperbolization and virtual
bundle conjectures to some algebraic conjectures about certain 3-manifold
groups.
