On 2-knot groups with abelian commutator subgroups

Abstract

In this paper it is shown that if the commutator subgroup of a 2 2 -knot group is abelian, then it is isomorphic to Z ⊕ Z ⊕ Z Z \oplus Z \oplus Z , Z α {Z_\alpha } , Z [ 1 / 2 ] Z[1/2] or Z [ 1 / 2 ] ⊕ Z 5 Z[1/2] \oplus {Z_5} , where α \alpha is an odd integer and Z [ 1 / 2 ] Z[1/2] is the additive group of the dyadic rationals.