  An exact-diagonalization technique on small clusters is used to study the
ground state of the dimerized t-J model at quarter filling. The equal-time
charge and spin correlations, charge and spin gaps, and binding energy are
calculated for the two-dimensional lattice with a spatial dimerization pattern
corresponding to organic conductors $\kappa-(BEDT-TTF)_2X$. We show that
competition between the effects of two types of dimerization, i.e.,
dimerization in the hopping integral and dimerization in the exchange
interaction, leads to the insulator-superconductor transition in the ground
state of the model. The phase diagram is thereby presented.
