Abstract: By a celebrated theorem of Lelong-Ferrand, proving a conjecture of Lichnerowicz, a compact Riemannian manifold with noncompact conformal group is conformally equivalent to the round sphere. The "pseudo-Riemannian Lichnerowicz conjecture," that a compact pseudo-Riemannian manifold (M,g) with essential conformal group is conformally flat, remains open. I will present a tight upper bound on the nilpotence degree of a connected nilpotent subgroup of Conf(M,g) and a theorem that if this maximal degree is attained, then M is conformally flat---and in fact is essentially a quotient of the Moebius space, the compact model space for pseudo-Riemannian conformal geometry analogous to the sphere. These results support the generalized Lichnerowicz conjecture.