Generalized torsion elements in the knot groups of twist knots

preprint2015arXivOpen access

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 525_2, which is the (−2)(-2)-twist knot, by Naylor and Rolfsen.

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