AI 中文总结
研究有限厚广义四边形\(\SA\)，\(G\leq \Aut(\SA)\)在点和线本原作用且基座为\(\PSp_4(q)\)（\(q\geq3\)），通过几乎单约化，证明\(\SA\)对偶下是经典辛四边形\(W(3,q)\)。
AI 中文摘要
设\(\SA\)为有限厚广义四边形，\(G\leq \Aut(\SA)\)在点和线上都本原作用。基于点本原和线本原作用的几乎单约化，研究\(G\)的基座为射影辛群\(\PSp_4(q)\)（\(q\geq3\)）的情形。证明此假设迫使\(\SA\)对偶意义下为经典辛四边形\(W(3,q)\)。
英文摘要
Let $\mc{S}$ be a finite thick generalized quadrangle, and let $G\leq \Aut(\mc{S})$ act primitively on both points and lines. Building on the almost simple reduction for point-primitive and line-primitive actions, we study the case where the socle of $G$ is the projective symplectic group $\PSp_4(q)$ with $q\ge 3$. We show that, up to duality, either $\mc{S}\cong W(3,q)$ for $q\geq 3$, or $q=3$ and $\mc{S}\cong H(3,4)$.
