Skobeltsyn Institute of Nuclear Physics,

Lomonosov Moscow State University,

119992 Moscow,

RUSSIA

and

Institute for Theoretical Physics,

University of G\"ottingen,

D-37077 G\"ottingen,

GERMANY

E-mail: bogoslov@theory.sinp.msu.ru, goenner@theorie.physik.uni-goettingen.de

**Subgroups of the group of generalized Lorentz transformations
and their geometric invariants**

**Abstract:**

Finite transformations belonging to two noncompact subgroups of the
group of generalized Lorentz transformations are found in an explicit form.
The group of generalized Lorentz transformations is the linear group, which
leaves invariant the metric of a flat Finslerian event space with a partially
broken 3D isotropy as well as the corresponding nonlinear generalized Dirac
equation. The above-mentioned subgroups play a key role in constructing
exact solutions of such an equation.