  This paper gives an algebraic conjecture which is shown to be equivalent to
Thurston's Geometrization Conjecture for closed, orientable 3-manifolds. It
generalizes the Stallings-Jaco theorem which established a similar result for
the Poincare Conjecture. The paper also gives two other algebraic conjectures;
one is equivalent to the finite fundamental group case of the Geometrization
Conjecture, and the other is equivalent to the union of the Geometrization
Conjecture and Thurston's Virtual Bundle Conjecture.
