In this paper, the connections between model theory and the theory of
infinite permutation groups are used to study the n-existence and the
n-uniqueness for n-amalgamation problems of stable theories. We show that, for
any n>1, there exists a stable theory having (k+1)-existence and k-uniqueness,
for every k<n+1, but that does not have neither (n+2)-existence nor
(n+1)-uniqueness. In particular, this generalizes the example, for n=2, due to
E.Hrushovski given in [3].