  In this paper we show that the nontrivial fundamental group $\pi_1 SO(3)
={\Bbb Z}_2$ for the group SO(3) of global proper rotations of a
four-dimensional Euclidian space (when a spin structure is introduced
preliminarily in that space) implies always fermions as global SO(3) vortices,
while bosons can be reduced to trivial lines (contracted into a point) in the
SO(3) group space.
