The hypergroups H of type U on the right can be classified in terms of the family P1 ={1◦x/xϵH}, where 1 ϵ H is the right scalar identity. If the size of H is 5, then P1 can assume only 6 possible values, three of which have been studied in [3]. In this paper, we completely describe other two of the remaining possible cases: a) P1 ={{1},{2,3},{4},{5}}; b) P1 ={{1},{2,3},{4,5}}. In these cases, P1 is a partition of H and the equivalence relation associated to it is a regular equivalence on H. We find that, apart of somorphisms, there are exactly 41 hypergroups in case a), and 56 hypergroups in case b).

Hypergroups of type U on the right of size five Part two

DE SALVO, Mario;LO FARO, Giovanni
2008-01-01

Abstract

The hypergroups H of type U on the right can be classified in terms of the family P1 ={1◦x/xϵH}, where 1 ϵ H is the right scalar identity. If the size of H is 5, then P1 can assume only 6 possible values, three of which have been studied in [3]. In this paper, we completely describe other two of the remaining possible cases: a) P1 ={{1},{2,3},{4},{5}}; b) P1 ={{1},{2,3},{4,5}}. In these cases, P1 is a partition of H and the equivalence relation associated to it is a regular equivalence on H. We find that, apart of somorphisms, there are exactly 41 hypergroups in case a), and 56 hypergroups in case b).
2008
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/1835358
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 9
  • ???jsp.display-item.citation.isi??? ND
social impact