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

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Author(s): Rosa Stangarone | Antonio Terrusi

Journal: Le Matematiche
ISSN 0373-3505

Volume: 44;
Issue: 1;
Start page: 97;
Date: 1989;
Original page

ABSTRACT
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.
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