Free quandles and knot quandles are residually finite
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- by Valeriy G. Bardakov, Mahender Singh and Manpreet Singh PDF
- Proc. Amer. Math. Soc. 147 (2019), 3621-3633 Request permission
Abstract:
In this note, residual finiteness of quandles is defined and investigated. It is proved that free quandles and knot quandles of tame knots are residually finite and Hopfian. Residual finiteness of quandles arising from residually finite groups (conjugation, core, and Alexander quandles) is established. Further, residual finiteness of automorphism groups of some residually finite quandles is also discussed.References
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Additional Information
- Valeriy G. Bardakov
- Affiliation: Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, 630090, Novosibirsk, Russia; Novosibirsk State University, 2 Pirogova Street, 630090, Novosibirsk, Russia; Novosibirsk State Agrarian University, Dobrolyubova Street, 160, Novosibirsk, 630039, Russia
- MR Author ID: 328717
- Email: bardakov@math.nsc.ru
- Mahender Singh
- Affiliation: Department of Mathematical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, S. A. S. Nagar, P. O. Manauli, Punjab 140306, India
- MR Author ID: 838614
- Email: mahender@iisermohali.ac.in
- Manpreet Singh
- Affiliation: Department of Mathematical Sciences, Indian Institute of Science Education and Research (IISER) Mohali, Sector 81, S. A. S. Nagar, P. O. Manauli, Punjab 140306, India
- Email: manpreetsingh@iisermohali.ac.in
- Received by editor(s): May 20, 2018
- Received by editor(s) in revised form: November 22, 2018
- Published electronically: April 8, 2019
- Additional Notes: The first author acknowledges support from the Russian Science Foundation project N 16-41-02006.
The second author acknowledges support from INT/RUS/RSF/P-02 grant and SERB Matrics Grant.
The third author thanks IISER Mohali for the PhD Research Fellowship. - Communicated by: David Futer
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 3621-3633
- MSC (2010): Primary 57M25; Secondary 20E26, 57M05, 20N05
- DOI: https://doi.org/10.1090/proc/14488
- MathSciNet review: 3981139