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The Symmetry of Lower and Upper Approximations, Determined by a Cyclic Hypergroup, Applicable in Control Theory
Open AccessArticle

On Hypergroups with a β-Class of Finite Height

Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università di Messina, 98166 Messina, Italy
Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Università di Udine, 33100 Udine, Italy
Author to whom correspondence should be addressed.
Symmetry 2020, 12(1), 168;
Received: 13 December 2019 / Revised: 7 January 2020 / Accepted: 10 January 2020 / Published: 15 January 2020
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. View Full-Text
Keywords: hypergroup; semihypergroup; 1-hypergroup; fundamental relation; height hypergroup; semihypergroup; 1-hypergroup; fundamental relation; height
MDPI and ACS Style

De Salvo, M.; Fasino, D.; Freni, D.; Lo Faro, G. On Hypergroups with a β-Class of Finite Height. Symmetry 2020, 12, 168.

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