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The groups $G_n^k$ were defined by V. O. Manturov in order to describedynamical systems in configuration systems. In the paper we consider twoapplications of this theory: we define a biquandle structure on the groups$G_n^k$, and construct a homomorphism from the surface singular braid monoid tothe group $G_n^2$.

On biquandles for the groups $G_n^k$ and surface singular braid monoid