In this paper, we introduce the new construction of quandles. For a group G and a subset A
of G we construct a quandle Q (G, A) which is called the (G, A)-quandle and study properties …

The paper develops the theory of quandle rings introduced by the authors in a recent work.
Orderability of quandles is investigated and many interesting examples of such quandles …

Given a virtual biquandle multi-switch (S, V) on an algebraic system X (from some category)
and a virtual link L, we introduce a general approach to construct an algebraic system XS, V …

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 …

This paper is a first step in constructing the category of braided sets and its closest relative,
the category of Yang–Baxter sets. Our main emphasis is on the construction of morphisms …

We undertake the study of profinite quandles. We provide several constructions of profinite
quandles from profinite groups, and from other profinite quandle. We characterize which …

Quandles are self-distributive, right-invertible, idempotent algebras. A group with
conjugation for binary operation is an example of a quandle. Given a quandle $(Q,\ast) …

In this paper, we investigate residual finiteness and subquandle separability of quandles.
The existence of these finiteness properties implies the solvability of the word problem and …

This article fully characterize the residual finiteness of conjugation quandles of the
Baumslag-Solitar groups. The key difference between groups and their derived conjugation …

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 …