We give simple arithmetic conditions that force the Sylow p-subgroup of the critical group of a strongly regular graph to take a specific form. These conditions depend only on the parameters $(v,k,\lambda ,\mu )$ of the strongly regular graph under consideration. We give many examples, including how the theory can be used to compute the critical group of Conway's 99-graph and to give an elementary argument that no $srg(28,9,0,4)$ exists.

中文翻译：

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来自强正则图的参数的关键组结构

我们给出了简单的算术条件，这些条件迫使强正则图的关键群的Sylow p-子群采取特定形式。这些条件仅取决于参数$（v，ķ，\lambda ，\mu ）$正在考虑的强正则图。我们提供了许多示例，包括如何使用该理论来计算Conway 99张图的关键组并给出基本论点，即$s\mathrm{[R}G（28，9，0，4）$ 存在。