Homomorphisms of sd-hypergroups

An sd (sum-difference)-hypergroup is an hypergroup for which the operation is defined as follows: xy={x+y,|x−y|} . Here x and y belong to the positive cone of an abelian totally ordered group G . Such a structure is denoted by H(G) . In this paper the author solves a particular case of a problem about homomorphisms f:H(G)→H(G ′) posed and partially answered by P. Corsini [Rend. Sem. Mat. Univ. Padova 52 (1974), 117--140; MR0422482 (54 #10469)].