  It is shown that the group of generalized Lorentz transformations serves as
relativistic symmetry group of a flat Finslerian event space. Being the
generalization of Minkowski space, the Finslerian event space arises from the
spontaneous breaking of initial gauge symmetry and from the formation of
anisotropic fermion-antifermion condensate. The principle of generalized
Lorentz invariance enables exact taking into account the influence of
condensate on the dynamics of fundamental fields. In particular, the
corresponding generalized Dirac equation turns out to be nonlinear. We have
found two noncompact subgroups of the group of generalized Lorentz symmetry and
their geometric invariants. These subgroups play a key role in constructing
exact solutions of such equation.
