Next Article in Journal
The Generalized Distance Spectrum of the Join of Graphs
Previous Article in Journal
A Novel Integrated Subjective-Objective MCDM Model for Alternative Ranking in Order to Achieve Business Excellence and Sustainability
Previous Article in Special Issue
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

1
Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università di Messina, 98166 Messina, Italy
2
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; https://doi.org/10.3390/sym12010168
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.

Show more citation formats Show less citations formats
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop