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Generalized Torsion in Knot Groups

Published online by Cambridge University Press:  20 November 2018

Geoff Naylor  and
Dale Rolfsen
Geoff Naylor
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC e-mail: naylord@gmail.com e-mail: rolfsen@math.ubc.ca
Dale Rolfsen
Affiliation:
Department of Mathematics, University of British Columbia, Vancouver, BC e-mail: naylord@gmail.com e-mail: rolfsen@math.ubc.ca
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Abstract

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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.

Keywords

57M2732S5529F60knot groupgeneralized torsionordered group
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 59 , Issue 1 , 01 March 2016 , pp. 182 - 189
Copyright
Copyright © Canadian Mathematical Society 2016

References

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