  We investigate the effect of $Z_2$ magnetic monopoles and vortices on the
finite temperature deconfinement phase transition in the fundamental - adjoint
SU(2) lattice gauge theory. In the limit of complete suppression of the $Z_2$
monopoles, the mixed action for the SU(2) theory in its Villain form is shown
to be self-dual under the exchange of the fundamental and adjoint couplings. By
further suppressing the $Z_2$ vortices we show that the extended model reduces
to the Wilson action with a modified coupling. The universality of the SU(2)
deconfinement phase transition with the Ising model is therefore expected to
remain intact in the entire plane of the fundamental-adjoint couplings in the
continuum limit. The self-duality arguments related to the suppression of $Z_2$
monopoles are also applicable to the Villain form of mixed action for the SU(N)
theory with $Z_{N}$ magnetic monopoles.
