  The phase diagram of the multiple-spin exchange model on the triangular
lattice is studied using exact diagonalizations. The two-spin (J_2) and
four-spin (J_4) exchanges have been taken into account for 12, 16, 19, 21, 24,
and 27 site samples in the parameter region J_4=0 - 0.25 (for a fixed J_2=1).
It is found that the three-sublattice N\'eel ordered state built up by the pure
two-spin exchange can be destroyed by the four-spin exchange, forming a
spin-liquid state. The different data suggest that the phase diagram in this
range of parameters exhibits two phases. The pure J_2 phase is a
three-sublattice Neel ordered phase, a small J_4 drives it into a spin-liquid
state with a spin gap filled of a large number of singlets. This spin-liquid
phase is not of the same generic kind as the phase studied by Misguich et al.
[Phys. Rev. B 60, 1064 (1999)]. It is observed on the finite-size samples that
the spin liquid phase, as the Neel ordered phase, exhibits a magnetization
plateau at m = 1/3, and for J_4 >0.15 a second plateau atm=1/2. These two
plateaus are associated respectively to the semi-classical orderings uud and
uuud.
