On biquandles for the groups Gnk and surface singular braid monoid

The groups [Formula: see text] were defined by Manturov [V. O. Manturov and I. M. Nikonov, On braids and groups [Formula: see text], J. Knot Theory Ramif. 24(13) (2015) 1541009.] in order to describe dynamical systems in configuration systems. In the paper we consider two applications of this theory: we define a biquandle structure on the groups [Formula: see text], and construct a homomorphism from the surface singular braid monoid to the group [Formula: see text].