Generalized torsion elements in the knot groups of twist knots

TL;DR

This paper demonstrates that the knot groups of all negative twist knots contain generalized torsion elements, extending previous results known for specific cases like the $5_2$ knot.

Contribution

It generalizes the existence of generalized torsion elements from specific knots to all negative twist knots.

Findings

Negative twist knot groups admit generalized torsion elements

Extends previous results from the $5_2$ knot to all negative twist knots

Shows that knot groups can have torsion-like properties without being torsion groups

Abstract

It is well known that any knot group is torsion-free, but it may admit a generalized torsion element. We show that the knot group of any negative twist knot admits a generalized torsion element. This is a generalization of the same claim for the knot $5_2$, which is the $(-2)$-twist knot, by Naylor and Rolfsen.