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

Vito Abatangelo;Larato, Bambina
1996

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11589/2575
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