In every hypergroup, the equivalence classes modulo the fundamental relation β are the union of hyperproducts of element pairs. Making use of this property, we introduce the notion of height of a β-class and we analyze properties of hypergroups where the height of a β-class coincides with its cardinality. As a consequence, we obtain a new characterization of 1-hypergroups. Moreover, we define a hierarchy of classes of hypergroups where at least one β-class has height 1 or cardinality 1, and we enumerate the elements in each class when the size of the hypergroups is n ≤ 4, apart from isomorphisms.

On hypergroups with a β-class of finite height

De Salvo M.
Primo
;
Freni D.
Penultimo
;
Lo Faro G.
Ultimo
2020-01-01

Abstract

In every hypergroup, the equivalence classes modulo the fundamental relation β are the union of hyperproducts of element pairs. Making use of this property, we introduce the notion of height of a β-class and we analyze properties of hypergroups where the height of a β-class coincides with its cardinality. As a consequence, we obtain a new characterization of 1-hypergroups. Moreover, we define a hierarchy of classes of hypergroups where at least one β-class has height 1 or cardinality 1, and we enumerate the elements in each class when the size of the hypergroups is n ≤ 4, apart from isomorphisms.
2020
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/3163000
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