### Abstract

Original language | English |
---|---|

Pages (from-to) | 329-343 |

Journal | Journal of the Australian Mathematical Society |

Volume | 76 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2004 |

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*Journal of the Australian Mathematical Society*,

*76*(3), 329-343. https://doi.org/10.1017/S1446788700009897

}

*Journal of the Australian Mathematical Society*, vol. 76, no. 3, pp. 329-343. https://doi.org/10.1017/S1446788700009897

**Some Remarks on Flocks.** / Bader, L.; O'Keefe, C.M.; Penttila, Tim.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Some Remarks on Flocks

AU - Bader, L.

AU - O'Keefe, C.M.

AU - Penttila, Tim

PY - 2004

Y1 - 2004

N2 - 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/ + m/ - 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.

AB - 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/ + m/ - 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.

U2 - 10.1017/S1446788700009897

DO - 10.1017/S1446788700009897

M3 - Article

VL - 76

SP - 329

EP - 343

JO - Journal of the Australian Mathematical Society

JF - Journal of the Australian Mathematical Society

SN - 1446-7887

IS - 3

ER -