Generalized torsion in knot groups

TL;DR

This paper demonstrates that many classical knot groups contain generalized torsion, which implies they are not bi-orderable, with examples including all torus knots, the knot 5_2, and their satellites.

Contribution

It establishes the presence of generalized torsion in a broad class of knot groups, extending understanding of their algebraic properties.

Findings

All torus knots have generalized torsion in their groups.

The hyperbolic knot 5_2's group contains generalized torsion.

Satellites of these knots also exhibit generalized torsion.

Abstract

We show that for many classical knots one can find generalized torsion in the fundamental group of its complement, commonly called the knot group. It follows that such a group is not bi-orderable. Examples include all torus knots, the (hyperbolic) knot $5_2$ and satellites of these knots.