2 research outputs found
On the Construction of Finite Projective Planes from Homology Semibiplanes
From a projective plane Î with involutory homology Ï„ one constructs an incidence system Î /Ï„ having as points and blocks the (Ï„) -orbits of length 2 on the points and lines of Î , and with incidence inherited from Î . Such incidence systems satisfy certain properties which, when taken as axioms, define the class of homology semibiplanes. We describe how one determines, in principle, whether a given homology semibiplane Σ is realizable as IÎ /Ï„ for some Î and Ï„ and, moreover, how many non-equivalent pairs (Î , Ï„) yield Σ. In case Î ' is Desarguesian of prime order we show that Î ' is characterized by its homology semibiplane; i.e. Î /Ï„ ≃ Î '/σ' implies Π≃ Î