  Solutions of the sourceless Einstein's equation with weak and strong
cosmological constants are discussed by using In\"on\"u-Wigner contractions of
the de Sitter groups and spaces. The more usual case corresponds to a weak
cosmological-constant limit, in which the de Sitter groups are contracted to
the Poincar\'e group, and the de Sitter spaces are reduced to the Minkowski
space. In the strong cosmological-constant limit, however, the de Sitter groups
are contracted to another group which has the same abstract Lie algebra of the
Poincar\'e group, and the de Sitter spaces are reduced to a 4-dimensional
cone-space of infinite scalar curvature, but vanishing Riemann and Ricci
curvature tensors. In such space, the special conformal transformations act
transitively, and the equivalence between inertial frames is that of special
relativity.
