1 citations · 3 across the 12 of their papers we have counts for
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Verbal quandles with one parameter
E. Markhinina, T. Nasybullov
We find all words in the free group , such that for every group and an element the algebraic system with the binary operation $*_{W,…
Virtual and universal braid groups, their quotients and representations
V. Bardakov, I. Emel'yanenkov, M. Ivanov +3
In the present paper we study structural aspects of certain quotients of braid groups and virtual braid groups. In particular, we construct and study linear representations $B_n\to…
Representations of flat virtual braids which do not preserve the forbidden relations
V. Bardakov, B. Chuzhinov, I. Emel'yanenkov +8
In the paper, we construct a representation of the flat virtual braid group on strands by automorphisms of the free group with $2…
Finite skew braces with solvable additive group
Ilya Gorshkov, Timur Nasybullov
A. Smoktunowicz and L. Vendramin conjectured that if is a finite skew brace with solvable additive group, then the multiplicative group of is solvable. In this short note w…
Quandles with orbit series conditions
Marco Bonatto, Alissa S. Crans, Timur Nasybullov +1
We introduce the notion of an orbit series in a quandle. Using this notion we define four families of quandles based on finiteness conditions on their orbit series. Intuitively, th…
General constructions of biquandles and their symmetries
Valeriy Bardakov, Timur Nasybullov, Mahender Singh
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-theor…