广义四边形的Singer群的一个判别准则和$\widetilde{\mathbf{C}_2}$ -建筑物中一致格的构造
A criterion concerning Singer groups of generalized quadrangles, and construction of uniform lattices in $\widetilde{\mathbf{C}_2}$-buildings
摘要：
我们描述了一个简单的标准来构建辛格群的佩恩导出的广义四边形，产生，作为一个推论，分类辛格群的经典佩恩导出的四边形的任何特征。这概括了最近的建设辛格群的这些四边形，提出了在一份文件中班贝格和朱迪奇。在线性情形和其他几种情形下，我们的分类是完全的。相反，似乎是一个共同的信念，我们表明，对于经典的Payne导出的四边形，不同的辛格群的数量是非常大的，甚至有界以下的指数函数的顺序的基域。我们的结果有直接的应用$\widetilde{\mathbf{C}_2}$ -建筑物的理论，这是在文章的最后解释。
英文摘要：
We describe a simple criterion to construct Singer groups of Payne-derived generalized quadrangles, yielding, as a corollary, a classification of Singer groups of the classical Payne-derived quadrangles in any characteristic. This generalizes recent constructions of Singer groups of these quadrangles that were presented in a paper by Bamberg and Giudici. In the linear case, and several other cases, our classification is complete. Contrary to what seemed to be a common belief, we show that for the classical Payne-derived quadrangles, the number of different Singer groups is extremely large, and even bounded below by an exponential function of the order of the ground field. Our results have direct applications to the theory of $\widetilde{\mathbf{C}_2}$-buildings, which are explained at the end of the paper.
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