New proofs are given of the fundamental results of Bader, Lunardon and Thas relating flocks of the quadratic cone in pg(3,q), q odd, and BLT-sets of Q(4,q). We also show that there is a unique BLT-set of H(3,9). The model of Penttila for Q(4,q) q odd, is extended to Q(2m,q) to construct partial flocks of size qm/2+m/2-1 of the cone K in pg(2m-1,q) with vertex a point and base Q(2m-2,q) , where q is congruent to 1 or 3 modulo 8 and m is even. These partial flocks are larger than the largest previously known for m>2 . Also, the example of O'Keefe and Thas of a partial flock of K in pg(5,3) of size 6 is generalised to a partial flock of the cone K of pg(2pn-1,p) of size 2pn , for any prime p congruent to 1 or 3 modulo 8, with the corresponding partial BLT-set of Q(2pn,p) admitting the symmetric group of degree 2pn+1 .
Some remarks on flocks / Bader, Laura; O'Keefe, C. M.; Penttila, T.. - In: JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY. - ISSN 1446-7887. - STAMPA. - 76:(2004), pp. 329-343.
Some remarks on flocks
BADER, LAURA;
2004
Abstract
New proofs are given of the fundamental results of Bader, Lunardon and Thas relating flocks of the quadratic cone in pg(3,q), q odd, and BLT-sets of Q(4,q). We also show that there is a unique BLT-set of H(3,9). The model of Penttila for Q(4,q) q odd, is extended to Q(2m,q) to construct partial flocks of size qm/2+m/2-1 of the cone K in pg(2m-1,q) with vertex a point and base Q(2m-2,q) , where q is congruent to 1 or 3 modulo 8 and m is even. These partial flocks are larger than the largest previously known for m>2 . Also, the example of O'Keefe and Thas of a partial flock of K in pg(5,3) of size 6 is generalised to a partial flock of the cone K of pg(2pn-1,p) of size 2pn , for any prime p congruent to 1 or 3 modulo 8, with the corresponding partial BLT-set of Q(2pn,p) admitting the symmetric group of degree 2pn+1 .File | Dimensione | Formato | |
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