We give two sufficient conditions for a hypergroupoid to be a feeble semi-hypergroupoid and a sufficient condition to be a feeble hypergroup. We show that every hypergroup in the class of the k-quasi-Steiner hypergroupoids is feebly associative. Finally, we apply these algebraic results to study Steiner systems; in particular, we give a necessary and sufficient condition for a Steiner system to be a projective plane.

A hypergroupal characterization of projective planes

GENTILE, GIUSEPPE
2000

Abstract

We give two sufficient conditions for a hypergroupoid to be a feeble semi-hypergroupoid and a sufficient condition to be a feeble hypergroup. We show that every hypergroup in the class of the k-quasi-Steiner hypergroupoids is feebly associative. Finally, we apply these algebraic results to study Steiner systems; in particular, we give a necessary and sufficient condition for a Steiner system to be a projective plane.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11570/1586281
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