A hypergroupal characterization of projective planes
type: Item
instance of: scholarly article
title: A hypergroupal characterization of projective planes
zbMATH Open document ID: 0951.20058
DOI: 10.1016/S0012-365X(99)00402-1
author: Giuseppe Gentile
published in: Discrete Mathematics
publication date: 2000-12-11T00:00:00Z
review text: The class of feebly associative hypergroupoids is a subclass of the \(H_v\)-semigroups. The Steiner systems are related in recent years with the theory of hyperstructures. Two sufficient conditions in order that a hypergroupoid should be a feebly semihypergroupoid and a sufficient condition to be a feebly hypergroup are proved. It is also proved that every hypergroup in the class of \(k\)-quasi-Steiner hypergroupoids is feebly associative. The paper concludes with a necessary and sufficient condition for a Steiner system to be a projective plane. The paper contains examples in all the above cases.
Mathematics Subject Classification ID: 20N20
Mathematics Subject Classification ID: 05B25
Mathematics Subject Classification ID: 51E10
Mathematics Subject Classification ID: 51E15
zbMATH DE Number: 1462276
zbMATH Keywords: feebly associative hypergroupoids
zbMATH Keywords: \(H_v\)-semigroups
zbMATH Keywords: Steiner systems
zbMATH Keywords: feebly hypergroups
zbMATH Keywords: \(k\)-quasi-Steiner hypergroupoids
zbMATH Keywords: projective planes
reviewed by: Thomas Vougiouklis
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1462276