On the hypergroups with four proper pairs and two or three non-scalar elements
type: Item
instance of: scholarly article
title: On the hypergroups with four proper pairs and two or three non-scalar elements
zbMATH Open document ID: 0878.20044
DOI: 10.1007/BF02844472
author: Mario De Salvo
author: Domenico Freni
author: Giovanni Lo Faro
publication date: 1997-11-11T00:00:00Z
review text: For a hypergroup \(H\) denote by \(P(H)=\{(x,y)\in H^2\mid|xy|\geq 2\}\), the set of all proper pairs of \(H\), and by \(S(H)=\{x\in H\mid|xy|=|yx|=1\), \(\forall y\in H\}\), the set of all scalars of \(H\). The authors determine (up to isomorphism) the hypergroups with four proper pairs which also verify the supplementary condition \(\text{Card}(S(H))\in\{2,3\}\). The problem of determination of all hypergroups \(H\) for which \(P(H)\) contains exactly four elements is difficult and for solving it it is necessary to develop long and laborious calculations. The authors surpass these difficulties in an elegant manner and finally obtain a classification of this type of hypergroups. The big variety of examples and the main result given in this paper can be considered as important tools for classifying all finite hypergroups.
Mathematics Subject Classification ID: 20N20
zbMATH DE Number: 1036016
zbMATH Keywords: groups of scalars
zbMATH Keywords: proper pairs
zbMATH Keywords: finite hypergroups
reviewed by: Marin Guţan
MaRDI profile type: Publication
cites work: Q5515384
cites work: Q3137919
cites work: On the hypergroups with four proper pairs and without scalars
cites work: On the hypergroups with four proper pairs and three or four non-scalar elements
cites work: Q4353306
cites work: Q3718946
cites work: Infinite hypergroups having a finite number of proper hyperproducts
full work available at URL: https://doi.org/10.1007/bf02844472
OpenAlex ID: W2090430586
published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 1036016