  We discuss dynamical breaking of non-abelian gauge groups in three
dimensional (lattice) gauge systems via the formation of fermion condensates. A
physically relevant example, motivated by condensed-matter physics, is that of
a fermionic gauge theory with group $SU(2)\otimes U_S(1) \otimes U_{E}(1)$. In
the strong U_S(1) region, the SU(2) symmetry breaks down to a U(1), due to the
formation of a parity-invariant fermion condensate. We conjecture a phase
diagram for the theory involving a critical line, which separates the regions
of broken SU(2) symmetry from those where the symmetry is restored. In the
broken phase, the effective Abelian gauge theory is closely related to an
earlier model of two-dimensional parity-invariant superconductivity in doped
antiferromagnets. The superconductivity in the model occurs in the
Kosterlitz-Thouless mode, since strong phase fluctuations prevent the existence
of a local order parameter. Some physical consequences of the $SU(2) \times
U_S(1)$ phase diagram for the (doping-dependent) parameter space of this
condensed-matter model are briefly discussed.
