Una generalizzazione di un teorema di B. Segre sui punti regolari rispetto ad una ellisse di un piano affine di Galois

Abstract

Let E be an ellipse in the affine plane AG(2, q), and let Γ be the cyclic linear collineation group of order q + 1 fixing E. The points of E form a single cycle under Γ. More generally, the points of E fall into cycles of the same size under the action of the subgroup Γ(d) of F of order d. If Ed) is one such cycle of sixe d and t is a point not on E, let nd (t) the number of chords of E(d) passing through t. An upper bound for nd (t) is obtained, from which we deduce, in the case d=(q + l)/2, a theorem of B. Segre [8].