Generalized quadrangles with a point-primitive and line-primitive automorphism group with socle \PSp₄(q)

2026/07/23 by Meizi Ou, Jianbing Lu
#math.CO

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Abstract

Let \SA be a finite thick generalized quadrangle, and let G≤ \Aut(\SA) 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 \PSp₄(q) with q≥ 3. We show that this hypothesis forces \SA to be the classical symplectic quadrangle W(3,q) up to duality.

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