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].
Una generalizzazione di un teorema di B. Segre sui punti regolari rispetto ad una ellisse di un piano affine di Galois / Abatangelo, Vito; Korchmáros, Gábor. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - STAMPA. - 172:1(1997), pp. 87-102. [10.1007/BF01782608]
Una generalizzazione di un teorema di B. Segre sui punti regolari rispetto ad una ellisse di un piano affine di Galois
Vito Abatangelo;
1997-01-01
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].I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
