Geometric hyperquasigroups and line spaces. (English) Zbl 0566.51016

Tallini, Giuseppe

Acta Univ. Carol., Math. Phys. 25, No. 1, 69-73 (1984).

The author associates with each projective space a hypergroup, i.e. a system where the product of two elements is a subset rather then another element. In the sequel, he assumes the hypergroup to be finite and derives arithmetic equalities and inequalities for appropriately defined parameters.
Unfortunately, no proofs are given and the reviewer was unable to see which of the relations given are trivial and which are not. It is also not clear why the language of hypergroups was introduced at all, as the results pertain to combinatorial geometry.

Reviewer: P.Wilker

MSC:

51E30	Other finite incidence structures (geometric aspects)
51E20	Combinatorial structures in finite projective spaces
20N99	Other generalizations of groups

Keywords:

geometric hyperquasigroups; projective space; combinatorial geometry