Free quandles and knot quandles are residually finite
Valeriy G. Bardakov, Mahender Singh, Manpreet Singh
TL;DR
This paper investigates the residual finiteness of various classes of quandles, proving that free and knot quandles are residually finite and Hopfian, and exploring residual finiteness in related algebraic structures.
Contribution
It establishes residual finiteness for free quandles, knot quandles, and quandles from residually finite groups, advancing understanding of their algebraic properties.
Findings
Free quandles are residually finite and Hopfian.
Knot quandles of tame knots are residually finite and Hopfian.
Quandles from residually finite groups are residually finite.
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.
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