Residual torsion-free nilpotence, bi-orderability, and two-bridge links

Abstract Residual torsion-free nilpotence has proved to be an important property for knot groups with applications bi-orderability and ribbon concordance. Mayland proposed a strategy show that two-bridge group commutator subgroup which is union of ascending chain para-free groups. This paper proves Mayland’s assertion expands the result subgroups link correspond kernels maps $\mathbb{Z}$ . We call these Alexander links. As result, we large family proof makes use modified version graph-theoretic construction Hirasawa Murasugi in order understand structure group.