Abstract
In [1] S. ILKKA conjectured that pqeudoregular points of an elliptic quadric ofAG(2,q),q odd, only exist for small values ofq. In [3] B. SEGRE ”proves” that an elliptic quadric ofAG(2,q),q odd, has pseudoregular points iffq=3 or 5. In [2], however, F. KáRTESZI shows that an elliptic quadric ofAG(2,7) has eight pseudoregular points. In this note we prove that part of B. Segre's proof is not correct, and that an elliptic quadric ofAG(2,q),q odd, has pseudoregular points iffq=3, 5 or 7.
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References
ILKKA, S.: On the inner and outer points of conics and between-essrelation in finite linear planes of odd characteristic.Report of the Helsinki University of Technology, Math., A 16 (1973).
KÁRTESZI, F.: Su una congettura di Seppo Ilkka.Ann. Univ. Sci. Budapest Rolando Eötvös, Sect. Math. 20 (1977), 167–175.
SEGRE, B.: Proprietà elementari relative ai segmenti ed alle coniche sopra un campo qualsiasi ed una congettura di Seppo Ilkka per il caso dei campi di Galois.Annali di matematica pura ed applicata, (IV), Vol. XCVI (1973), 289–337.
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Debroey, I. Note: A remark on a result of B. Segre concerning pseudoregular points of an elliptic quadric ofAG(2,q), q odd. J Geom 14, 159–163 (1980). https://doi.org/10.1007/BF01918529
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DOI: https://doi.org/10.1007/BF01918529