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# Generalized Torsion in Knot Groups

Published:2015-05-13
Printed: Mar 2016
• Geoff Naylor,
Department of Mathematics, University of British Columbia, Vancouver, BC
• Dale Rolfsen,
Department of Mathematics, University of British Columbia, Vancouver, BC
 Format: LaTeX MathJax PDF

## Abstract

In a group, a nonidentity element is called a generalized torsion element if some product of its conjugates equals the identity. 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 algebraic knots in the sense of Milnor.
 Keywords: knot group, generalized torsion, ordered group
 MSC Classifications: 57M27 - Invariants of knots and 3-manifolds 32S55 - Milnor fibration; relations with knot theory [See also 57M25, 57Q45] 29F60 - unknown classification 29F60

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