  Nonproduct n-qubit pure states with maximum dimensional stabilizer subgroups
of the group of local unitary transformations are precisely the generalized
n-qubit Greenberger-Horne-Zeilinger states and their local unitary equivalents,
for n greater than or equal to 3 but not equal to 4. We characterize the Lie
algebra of the stabilizer subgroup for these states. For n=4, there is an
additional maximal stabilizer subalgebra, not local unitary equivalent to the
former. We give a canonical form for states with this stabilizer as well.
