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Generalized torsion elements in the knot groups of twist knots


Author: Masakazu Teragaito
Journal: Proc. Amer. Math. Soc. 144 (2016), 2677-2682
MSC (2010): Primary 57M25; Secondary 57M05, 06F15
DOI: https://doi.org/10.1090/proc/12864
Published electronically: September 11, 2015
MathSciNet review: 3477085
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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.


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Additional Information

Masakazu Teragaito
Affiliation: Department of Mathematics and Mathematics Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-hiroshima, Japan 739-8524
Email: teragai@hiroshima-u.ac.jp

DOI: https://doi.org/10.1090/proc/12864
Received by editor(s): May 10, 2015
Received by editor(s) in revised form: June 12, 2015
Published electronically: September 11, 2015
Additional Notes: The author was partially supported by Japan Society for the Promotion of Science, Grant-in-Aid for Scientific Research (C), 25400093.
Communicated by: Martin Scharlemann
Article copyright: © Copyright 2015 American Mathematical Society