51 citations · 254 across the 64 of their papers we have counts for
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Constructions and automorphisms of quandles
Valeriy G. Bardakov, Birama Sangare
We prove that if M is an abelian group and X = Alex(M, phi) is a Latin Alexander quandle with id - phi in Aut(M), then Aut(X) is isomorphic to M semidirect C_Aut(M)(phi), Inn(X) is…
Multi-virtual braid groups
Valeriy G. Bardakov, Tatyana A. Kozlovskaya, Komal Negi +1
L. Kauffman (2024) introduced multi-virtual and symmetric multi-virtual braid groups, which are generalizations of the virtual braid group. We introduce multi-virtual pure and mult…
Cayley graphs and their growth functions for multivalued groups
Valeriy G. Bardakov, Tatyana A. Kozlovskaya, Matvei N. Zonov
We define the Cayley graph and its growth function for multivalued groups. We prove that if we change a finite set of generators of multivalued group, or change the starting point,…
Orders of Products of Slanted Class Transpositions
V. G. Bardakov, A. L. Iskra
In the present work, we continue the research initiated in the preprint: V. G. Bardakov, A. L. Iskra, Orders of products of horizontal class transpositions, arXiv:2409.13341, and r…
Orders of products of horizontal class transpositions
V. G. Bardakov, A. L. Iskra
The class transposition group was introduced by S. Kohl in 2010. It is a countable subgroup of the permutation group of the set of integers $\mat…
Lie Rota--Baxter operators on the Sweedler algebra
Valeriy G. Bardakov, Igor M. Nikonov, Viktor N. Zhelaybin
If is an associative algebra, then we can define the adjoint Lie algebra and Jordan algebra . It is easy to see that any associative Rota--Baxter operator on…