Two-knot groups with torsion free Abelian normal subgroups of rank two (Q1116499)

In an earlier paper [Comment. Math. Helv. 61, 122--148 (1986; Zbl 0611.57015)] the author showed that if a 2-knot group \(G\) has a torsion free abelian normal subgroup \(A\) of rank \(r\geq 2\), then in fact \(r=2, 3\), or \(4\). Furthermore he determined the groups admitting such a subgroup with \(r=3\) or \(4\). This paper concentrates on the case \(r=2\), and begins by showing that if \(A\) is also contained in the commutator subgroup \(G'\), then \(A\) must be finitely generated. Moreover, it is shown that the centralizer of \(A\) is not contained in \(G'\), and that neither of these groups is finitely generated. Finally, an algebraic characterization is given of the groups of 2-knots which are cyclic branched covers of twist spun torus knots. As the author remarks, these provide all the known examples of such subgroups \(A\) with \(r=2\).