Ovoids of \(\mathcal{H}(3, q^2)\), \(q\) odd, admitting a group of order \(\frac{(q + 1)^3}{2}\)
type: Item
instance of: scholarly article
title: Ovoids of \(\mathcal{H}(3, q^2)\), \(q\) odd, admitting a group of order \(\frac{(q + 1)^3}{2}\)
zbMATH Open document ID: 1396.51003
author: Francesco Pavese
published in: Discrete Mathematics
publication date: 2018-05-24T00:00:00Z
review text: A \textit{generalised quadrangle} of order \((s, t )\) is a partial linear space with the properties that every point is incident with \(t + 1\) lines, every line is incident with \(s + 1\) points, and through any point \(P\), not on a line \(l\), there is a unique line intersecting \(l\). An \textit{ovoid} of a generalised quadrangle is a subset of its points which meets every line of the generalised quadrangle in exactly one point. The generalised quadrangle \(\mathcal{H}(3,q^2)\) consists of the points and lines of a non-degenerate Hermitian surface of \(\mathrm{PG}(3,q^2)\), it has order \((q^2,q)\). In this paper, a new construction of an ovoid \(\mathcal{O}\) of the Hermitian surface \(\mathcal{H}(3,q^2)\), \(q > 3\) odd, is provided. The stabiliser group of the ovoid is calculated; it depends on the particular elements \(a,b\) in \(\mathrm{GF}(q)\) that are used in the construction. But in all cases, the stabiliser of \(\mathcal{O}\) has a subgroup of order \((q+1)^3\). Finally, it is also shown that \(\mathcal{O}\) cannot be obtained from a Hermitian curve by means of multiple derivation and it is not locally Hermitian.
reviewed by: Geertrui Van de Voorde
Mathematics Subject Classification ID: 51E12
Mathematics Subject Classification ID: 51E20
zbMATH DE Number: 6872663
zbMATH Keywords: Hermitian surface
zbMATH Keywords: ovoid
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: j.disc.2018.04.013
OpenAlex ID: W2800611766
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DOI: 10.1016/J.DISC.2018.04.013
description: scientific article; zbMATH DE number 6872663