We determine a new family of hypergroups of type U on the right and find necessary and sufficient conditions so that such hypergroups are of type C on the right or cogroups. Moreover, we prove some fundamental properties of the family Pε = {εx | x ∈ H}, determined by the right scalar identity ε of a hypergroup H of type U on the right. If H has size five, then there exist six possibilities for the family Pε. In three of these cases, we find, up to isomorphisms, the tables of the corresponding hypergroups. The remaining cases will be studied in a forthcoming paper.
A new family of hypergroups and hypergroups of type U on the right of size five
DE SALVO, Mario;LO FARO, Giovanni
2007-01-01
Abstract
We determine a new family of hypergroups of type U on the right and find necessary and sufficient conditions so that such hypergroups are of type C on the right or cogroups. Moreover, we prove some fundamental properties of the family Pε = {εx | x ∈ H}, determined by the right scalar identity ε of a hypergroup H of type U on the right. If H has size five, then there exist six possibilities for the family Pε. In three of these cases, we find, up to isomorphisms, the tables of the corresponding hypergroups. The remaining cases will be studied in a forthcoming paper.File in questo prodotto:
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