RENDICONTI - ISTITUTO LOMBARDO. ACCADEMIA DI SCIENZE E LETTERE. A, SCIENZE MATEMATICHE E APPLICAZIONI
Abstract
The author continues the study of exchange hypergroups that he initiated in a previous work. A hypergroup H is called an exchange hypergroup if, for all A⊆H, x∈⟨A∪{y}⟩ and x∉⟨A⟩⇒y∈⟨A∪{x}⟩, where ⟨B⟩ denotes the intersection of all closed subhypergroups of H containing B. After proving some results of a general nature the author studies the relations between exchange hypergroups and the HG-hypergroups introduced by M. De Salvo . Finally he gives a characterization of exchange commutative groups: they are direct sums of cyclic groups of prime order.
