A hypergroupal characterization of projective planes (Q1567611)

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.