  We report on calculations of the heavy quark potential in SU(3) lattice gauge
theory. Full SU(3) results are compared to three cases which involve
gauge-fixing and projection. All of these start from the maximal abelian gauge
(MAG), in its simplest form. The first case is abelian projection to U(1)xU(1).
The second keeps only the abelian fields of monopoles in the MAG. The third
involves an additional gauge-fixing to the indirect maximal center gauge
(IMCG), followed by center projection to Z(3). At one gauge
fixing/configuration, the string tensions calculated from MAG U(1)xU(1), MAG
monopoles, and IMCG Z(3) are all less than the full SU(3) string tension. The
projected string tensions further decrease, by approximately 10%, when account
is taken of gauge ambiguities. Comparison is made with corresponding results
for SU(2). It is emphasized that the formulation of the MAG is more subtle for
SU(3) than for SU(2), and that the low string tensions may be caused by the
simple MAG form used. A generalized MAG for SU(3) is formulated.
