Ak-cap in PG(3,q) is a set of k points, no three of which are collinear. A k-cap is calledcomplete if it is not contained in a (k+1)-cap. The maximum valuem2(3, q) ofk for which there exists a k-cap in PG(3,q) is q2+1. Letm2(3, q) denote the size of the second largest complete k-cap in PG(3,q). This number is only known for the smallest values of q, namely for q=2, 3,4 (cf. [2], pp. 96–97 and [3], p. 303). In this paper we show thatm2(3,5)=20. We also prove that there are, up to isomorphism, only two complete 20-caps in PG(3,5) and determine their collineation groups.
Classification of maximal caps in PG(3,5), different from elliptic quadrics / Abatangelo, Vito; Gabor, Korchmaros; Larato, Bambina. - In: JOURNAL OF GEOMETRY. - ISSN 0047-2468. - STAMPA. - 57:1-2(1996), pp. 9-19. [10.1007/BF01229246]
Classification of maximal caps in PG(3,5), different from elliptic quadrics
Vito Abatangelo;Larato, Bambina
1996-01-01
Abstract
Ak-cap in PG(3,q) is a set of k points, no three of which are collinear. A k-cap is calledcomplete if it is not contained in a (k+1)-cap. The maximum valuem2(3, q) ofk for which there exists a k-cap in PG(3,q) is q2+1. Letm2(3, q) denote the size of the second largest complete k-cap in PG(3,q). This number is only known for the smallest values of q, namely for q=2, 3,4 (cf. [2], pp. 96–97 and [3], p. 303). In this paper we show thatm2(3,5)=20. We also prove that there are, up to isomorphism, only two complete 20-caps in PG(3,5) and determine their collineation groups.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
