On reductants of two groups

In this paper we consider the reductant of the dihedral group $D_n$, consisting of a set of axial symmetries, and the sphere $S^2$ as a reductant of the group $\mathrm{SU}(2, \mathbb{C}) \cong S^3$ (the group of unit quaternions). By introducing the Sabinin's multiplication on the reductant of $D_n$, we get a quasigroup with unit.