On the hypergroups with four proper pairs and three or four non-scalar elements

In this paper the authors studi the hypergroups, such that are exactly four pairs of elements, which define hyperproducts (i.e. with P(W)04), and such that there are three or four non-scalar elements. They solve the combinatorial problem of finding, up to isomorphism, all the tables of the aforesaid hypergroups and therefore, counting also on the papers [3], [4], they bring to a close the problem of finding all the finite hypegroups such that |P(H)|=4.