On metabelian two-knot groups

Abstract

We show that if the commutator subgroup of a 2 2 -knot group is abelian but not finitely generated, then it is isomorphic to the additive group of dyadic rationals, thus eliminating the one possibility left open in recent work of Yoshikawa. It follows that the examples given by Cappell and Fox provide a complete list of metabelian 2 2 -knot groups.