Sui q-archi completi di un piano non desarguesiano di ordine q pari

  • Rosa Stangarone
  • Antonio Terrusi


A classic theorem by B. Segre [4], and G. Tallini, [6], states that in a finite desarguesian plane of order q no complete q-arc exists. This result can not be extended to any non desarguesian plane ([1],[2],[3]).

In this paper we consider a non desarguesian plane πq of even order q greater or equal to 16 and we study complete q-arcs admitting one point of index q-4 in πq. As it is well known, [5], the admissible values for the index of the remaining points of πq are 0,2,4,6,8. We prove that the non existence of any point of index 8 implies q lesser or equal to 34.