Classification of maximal caps in PG(3,5) different from elliptic quadrics |
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Authors: | Vito Abatangelo Gabor Korchmaros Bambina Larato |
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Institution: | (1) Dipartimento di Matematica, Campus Univer., Via E. Orabona, 4, I 70125 Bari, Italia;(2) Dipartimento di Matematica, Via N. Sauro, 85, I 85100 Potenza, Italia |
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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 valuem
2(3, q) ofk for which there exists a k-cap in PG(3,q) is q2+1. Letm
2(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 thatm
2(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.In memoriam Giuseppe TalliniWork done within the activity of GNSAGA of CNR and supported by MURST. |
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Keywords: | 51E22 |
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