Geodesic
Generalized Torsion in Knot Groups
Canadian mathematical bulletin, Tome 59 (2016) no. 1, pp. 182-189

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DOI

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 ûnd 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.
DOI : 10.4153/CMB-2015-004-4
Mots-clés : 57M27, 32S55, 29F60, knot group, generalized torsion, ordered group 
Naylor, Geoff; Rolfsen, Dale. Generalized Torsion in Knot Groups. Canadian mathematical bulletin, Tome 59 (2016) no. 1, pp. 182-189. doi: 10.4153/CMB-2015-004-4
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