  In order to identify the most favorable situation for superconductivity in
the repulsive single-band Hubbard model, we have studied instabilities for
d-wave pairing mediated by antiferromagnetic spin fluctuations and p-pairing
mediated by ferromagnetic fluctuations with the fluctuation exchange
approximation in both two dimensions and three dimensions. By systematically
varying the band filling and band structure we have shown that (i) d-pairing is
stronger in two dimensions than in three dimensions, and (ii) p-pairing is much
weaker than the d-pairing.
