In this paper, we completely determine the point regular automorphism groups of the Payne derived quadrangle of the symplectic quadrangle $W(q)$, q odd. As a corollary, we show that the finite groups that act regularly on the points of a finite generalized quadrangle can have unbounded nilpotency class.

中文翻译：

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Payne导出W（q）的四边形的点正则自同构群。

在本文中，我们完全确定了辛四边形的Payne派生四边形的点正则同构群 $\mathrm{w\; ^}（q）$，q奇数。作为推论，我们证明了有规律地作用于有限广义四边形的点上的有限群可以具有无穷大的幂等性类。