广义四边形与传递伪超椭圆
Generalised quadrangles and transitive pseudo-hyperovals
摘要：
射影空间$\PG(3n-1,q)$的伪超椭圆，甚至$q$，是一组$n-1$维的$q^n+2$子空间，使得任意三个子空间跨越整个空间。证明了具有不可约传递稳定子的伪超卵形是初等的。然后，我们从这个结果推导出一个分类的厚广义四边形$\mathcal{Q}$，承认一个点本原，线传递自同构群的点正则阿贝尔正规子群。具体来说，我们表明，$\mathcal{Q}$是标志传递和同构的$T_2^*(\mathcal{H})$，其中$\mathcal{H}$是定期超椭圆的$\PG(2,4)$或Lunelli-Sce超椭圆的$\PG(2,16)$。
英文摘要：
A pseudo-hyperoval of a projective space $\PG(3n-1,q)$, $q$ even, is a set of $q^n+2$ subspaces of dimension $n-1$ such that any three span the whole space. We prove that a pseudo-hyperoval with an irreducible transitive stabiliser is elementary. We then deduce from this result a classification of the thick generalised quadrangles $\mathcal{Q}$ that admit a point-primitive, line-transitive automorphism group with a point-regular abelian normal subgroup. Specifically, we show that $\mathcal{Q}$ is flag-transitive and isomorphic to $T_2^*(\mathcal{H})$, where $\mathcal{H}$ is either the regular hyperoval of $\PG(2,4)$ or the Lunelli--Sce hyperoval of $\PG(2,16)$.
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