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Infinite hypergroups having a finite number of proper hyperproducts. (Hypergroupes infinis ayant un nombre fini d’hyperproduits propres.) (French) Zbl 0832.20085

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.

MSC:

20N20 Hypergroups
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