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
2000-01-01
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.File in questo prodotto:
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