Infinite hypergroups having a finite number of proper hyperproducts
For non-commutative hypergroups a theorem of P. Corsini (1980) is proved: If \((H, \cdot)\) is an infinite hypergroup with finite set of hyperproducts of cardinality greater than 1, then there exists \((a,b) \in H^2\) with \(\text{card} (a\cdot b) = \text{card }H\). Moreover, all hypergroups having at most two proper hyperproducts are determined. Therefore, these hypergroups include the very thin ones.
scientific article; zbMATH DE number 722327