Two-knot groups with torsion free abelian normal subgroups of rank two

We show that a torsion free abelian normal subgroup of rank two of a two-knot group which is contained in the commutator subgroup must be free abelian, the centralizer of the abelian subgroup is not contained in the commutator subgroup, and neither of the latter two groups is finitely generated. Furthermore, we characterize algebraically the groups of 2-knots which are cyclic branched covers of twist spun torus knots.