Residual torsion-free nilpotence, biorderability and pretzel knots

The residual torsion-free nilpotence of the commutator subgroup a knot group has played key role in studying bi-orderability groups. A technique developed by Mayland provides sufficient condition for to be residually-torsion-free nilpotent using work Baumslag. In this paper, we apply Mayland's several genus one pretzel knots and family with arbitrarily high genus. As result, obtain large number new examples bi-orderable These are first groups which not fibered or alternating.