  A complete orthonormal basis of N-qutrit unitary operators drawn from the
Pauli Group consists of the identity and 9^N-1 traceless operators. The
traceless ones partition into 3^N+1 maximally commuting subsets (MCS's) of
3^N-1 operators each, whose joint eigenbases are mutually unbiased. We prove
that Pauli factor groups of order 3^N are isomorphic to all MCS's, and show how
this result applies in specific cases. For two qutrits, the 80 traceless
operators partition into 10 MCS's. We prove that 4 of the corresponding basis
sets must be separable, while 6 must be totally entangled (and Bell-like). For
three qutrits, 728 operators partition into 28 MCS's with less rigid structure
allowing for the coexistence of separable, partially-entangled, and totally
entangled (GHZ-like) bases. However, a minimum of 16 GHZ-like bases must occur.
Every basis state is described by an N-digit trinary number consisting of the
eigenvalues of N observables constructed from the corresponding MCS.
