Free quandles and knot quandles are residually finite-Reference-Cited by-同舟云学术

Free quandles and knot quandles are residually finite

Published:2019-04-08 Issue:8 Volume:147 Page:3621-3633
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Bardakov Valeriy,Singh Mahender,Singh Manpreet

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.

Funder

Department of Science and Technology, Ministry of Science and Technology

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

https://www.ams.org/proc/2019-147-08/S0002-9939-2019-14488-9/proc14488_AM.pdf

Reference25 articles.

1. Automorphism groups of quandles arising from groups;Bardakov, Valeriy G.;Monatsh. Math.,2017

2. V. G. Bardakov, T. Nasybullov and M. Singh, Automorphism groups of quandles and related groups, Monatsh. Math. (2018), https://doi.org/10.1007/s00605-018-1202-y.

3. The word problem for finitely presented quandles is undecidable;Belk, James,2015