# Free quandles and knot quandles are residually finite

@article{Bardakov2019FreeQA, title={Free quandles and knot quandles are residually finite}, author={Valeriy G. Bardakov and Mahender Singh and Manpreet Singh}, journal={Proceedings of the American Mathematical Society}, year={2019} }

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.

## 7 Citations

Link quandles are residually finite

- MathematicsMonatshefte für Mathematik
- 2019

Residual finiteness is known to be an important property of groups appearing in combinatorial group theory and low dimensional topology. In a recent work (Bardakov et al. in Proc Am Math Soc…

Zero-divisors and idempotents in quandle rings

- Mathematics
- 2020

The paper develops further the theory of quandle rings which was introduced by the authors in a recent work. Orderability of quandles is defined and many interesting examples of orderable quandles…

General constructions of biquandles and their symmetries

- MathematicsJournal of Pure and Applied Algebra
- 2021

Biquandles are algebraic objects with two binary operations whose axioms encode the generalized Reidemeister moves for virtual knots and links. These objects also provide set-theoretic solutions of…

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