  We evaluate the dominant superconducting pairing symmetry in some
3-dimensional cubic lattice struct ures within the third-order perturbation
theory with respect to the on-site coulomb repulsion. We cl arify whether the
vertex correction term, which has a critical contribution to the p-wave state
in t he 2-dimensional systems, is also important in the 3-dimensional system.
We finally investigate the interplay between dimensionality and the vertex
correction to grasp common features independent of t he lattice structures in
the mechanism of the superconductivity.
