A generalization of a theorem of Griffiths to 3-manifolds

We generalize a result of Griffiths to 3-manifolds. Griffithsʹ theorem can be stated as follows: Let M be a 2-manifold whose fundamental group G contains a finitely generated subgroup U such that • ains a nontrivial normal subgroup N of G; f infinite index in G. M is the torus or Klein bottle.