  It is shown that in Minkowski space there exist transformations of the
coordinates of events alternative to the 3-parameter Lorentz boosts. However,
in contrast to the boosts, they constitute a 3-parameter noncompact group
which, in turn, is a subgroup of the homogeneous 6-parameter Lorentz group.
Moreover, in the same space, there exists another 3-parameter noncompact group
isomorphic to above-mentioned one. As we shall see, these two 3-parameter
noncompact groups are rudiments of the 3-parameter groups of relativistic
symmetry of the axially symmetric Finslerian spaces with the preferred
directions $\boldsymbol\nu$ and $-\boldsymbol\nu$, respectively. Finally, it
will be also demonstrated that inversion of the preferred direction
$\boldsymbol\nu$ in the axially symmetric Finslerian space-time does not change
the Lobachevski geometry of 3-velocity space. However, this leads to an
inversion of the corresponding family of horospheres of the space.
