G -Hypergroups: Hypergroups with a Group-Isomorphic Heart

Mario De Salvo, Dario Fasino, Domenico Freni and Giovanni Lo Faro
Additional contact information
Mario De Salvo: Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università di Messina, 98122 Messina, Italy
Dario Fasino: Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Università di Udine, 33100 Udine, Italy
Domenico Freni: Dipartimento di Scienze Matematiche, Informatiche e Fisiche, Università di Udine, 33100 Udine, Italy
Giovanni Lo Faro: Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università di Messina, 98122 Messina, Italy

Mathematics, 2022, vol. 10, issue 2, 1-17

Abstract: Hypergroups can be subdivided into two large classes: those whose heart coincide with the entire hypergroup and those in which the heart is a proper sub-hypergroup. The latter class includes the family of 1-hypergroups, whose heart reduces to a singleton, and therefore is the trivial group. However, very little is known about hypergroups that are neither 1-hypergroups nor belong to the first class. The goal of this work is to take a first step in classifying G -hypergroups, that is, hypergroups whose heart is a nontrivial group. We introduce their main properties, with an emphasis on G -hypergroups whose the heart is a torsion group. We analyze the main properties of the stabilizers of group actions of the heart, which play an important role in the construction of multiplicative tables of G -hypergroups. Based on these results, we characterize the G -hypergroups that are of type U on the right or cogroups on the right. Finally, we present the hyperproduct tables of all G -hypergroups of size not larger than 5, apart of isomorphisms.

Keywords: hypergroups; heart; group action; 1-hypergroups; cogroups (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/2/240/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/2/240/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:2:p:240-:d:724001

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().