论文标题
用$ \ mathrm {psl}（2，q）$作为一个自动形态组的有限通用四边形
On finite generalized quadrangles with $\mathrm{PSL}(2,q)$ as an automorphism group
论文作者
论文摘要
令$ \ mathcal {s} $为有限的厚实四边形，并假设$ g $是$ \ MATHCAL {S} $的自动形态组。如果$ g $在$ \ Mathcal {s} $的点和行上都可以原始起作用，那么众所周知，$ g $几乎必须很简单。在本文中，我们表明，如果$ g $的socle是$ \ mathrm {psl}（2，q）$，带有$ q \ geq4 $，则$ q = 9 $和$ \ mathcal {s} $是独特的普通式四边形Quadrangle，$ 2 $ 2 $。
Let $\mathcal{S}$ be a finite thick generalized quadrangle, and suppose that $G$ is an automorphism group of $\mathcal{S}$. If $G$ acts primitively on both the points and lines of $\mathcal{S}$, then it is known that $G$ must be almost simple. In this paper, we show that if the socle of $G$ is $\mathrm{PSL}(2,q)$ with $q\geq4$, then $q=9$ and $\mathcal{S}$ is the unique generalized quadrangle of order $2$.
