Generalized torsion elements in the knot groups of twist knots
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- by Masakazu Teragaito
- Proc. Amer. Math. Soc. 144 (2016), 2677-2682
- DOI: https://doi.org/10.1090/proc/12864
- Published electronically: September 11, 2015
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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.References
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Bibliographic Information
- Masakazu Teragaito
- Affiliation: Department of Mathematics and Mathematics Education, Hiroshima University, 1-1-1 Kagamiyama, Higashi-hiroshima, Japan 739-8524
- MR Author ID: 264744
- Email: teragai@hiroshima-u.ac.jp
- 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
- © Copyright 2015 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 2677-2682
- MSC (2010): Primary 57M25; Secondary 57M05, 06F15
- DOI: https://doi.org/10.1090/proc/12864
- MathSciNet review: 3477085