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A Distance-2-Spread of the Generalized Hexagon H(3)

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Abstract

In this paper, we construct a distance-2-spread of the known generalized hexagon of order 3 (the split Cayley hexagon H(3)). Furthermore we prove the uniqueness of this distance-2-spread in H(3) and show that its automorphism group is the linear group L2(13). We remark that a distance-2-spread in any split Cayley hexagon H(q) is a line spread of the underlying polar space Q(6, q) and we construct a line spread of Q(6, 2) that is not a distance-2-spread in any H(2) defined on Q(6, 2).

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Authors and Affiliations

  1. Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281-S22, 9000, Gent, Belgium

    A. De Wispelaere & H. Van Meldeghem

Authors
  1. A. De Wispelaere
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  2. H. Van Meldeghem
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Correspondence to A. De Wispelaere or H. Van Meldeghem.

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AMS Subject Classification: 51E12.

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De Wispelaere, A., Van Meldeghem, H. A Distance-2-Spread of the Generalized Hexagon H(3). Ann. Combin. 8, 133–154 (2004). https://doi.org/10.1007/s00026-004-0211-9

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  • DOI: https://doi.org/10.1007/s00026-004-0211-9

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