Sui q-archi completi in piani non desarguesiani di ordine q dispari

Abstract

By a well know theorem of Segre [5] and G. Tallini [7], the q-arcs of the desarguesian plane , are not complete.In [1],[2],[3] it is shown that this theorem cannot be extended to any non-desarguesian plane.In this paper, the following theorem is proved: Let be a complete q-arc of a projective plane 𝜋 of order q. Denote by the number of those points P of 𝜋 for which the number of tangents of passing through P is j. Then when ; for .