  We examine symplectic topological features of certain family of monotone
Lagrangian submanifolds in CP^n. Firstly, we give a cohomological restriction
for Lagrangian submanifolds in CP^n whose first integral homologies are
3-torsion. In particular, in the case where n=5,8, we prove the cohomologies
with coefficients in Z_2 of such Lagrangian submanifolds are isomorphic to that
of SU(3)/(SO(3) Z_3) and SU(3)/Z_3, respectively. Secondly, we calculate the
Floer cohomology of a monotone Lagrangian submanifold SU(p)/Z_p in CP^{p^2-1}
with coefficients in Z_2 by using Biran-Cornea's theory.
