  Monte Carlo simulation has been performed in the planar P(_{2}) and P(_{4})
models to investigate the effects of the suppression of topological defects on
the phase transition exhibited by these models. Suppression of the 1/2-defects
on the square plaquettes in the P(_{2}) model leads to complete elimination of
the phase transition observed in this model. However in the P(_{4}) model, on
suppressing the single 1/2-defects on square plaquettes, the otherwise first
order phase transition changes to a second order one which occurs at a higher
temperature and this is due to presence of large number of 1/2-pair defects
which are left within the square plaquettes. When we suppressed these charges
too, complete elimination of phase transition was observed.
