On knot-like groups and ribbon concordance (Q1207524)

E. S. Rapaport defined a knot-like group \(G\) to be finitely-presented, have deficiency one, and to abelianize to the infinite cyclic group. L. Neuwirth proved that if \(G\) is a knot group with finitely-generated commutator subgroup \(G'\), then \(G'\) is free. Rapaport has conjectured that this result holds for all knot-like groups. The first result of this paper is that Rapaport's conjecture is true for all knot-like 3-manifold groups. The second result is that it holds for all efficient ribbon concordance groups, a class of groups defined in the paper.