The orbital diameter of a primitive permutation group is the maximal diameter of its orbital graphs. There has been a lot of interest in bounds for the orbital diameter. In this paper we provide explicit bounds on the diameters of groups of simple diagonal type. As a consequence we obtain a classification of simple diagonal groups with orbital diameter less than or equal to 4. As part of this, we classify all finite simple groups with covering number and conjugacy width at most 3. We also prove some general bounds on the covering number and conjugacy width of groups of Lie type.

中文翻译：

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关于对角型群的轨道直径

原始置换群的轨道直径是其轨道图的最大直径。人们对轨道直径的界限很感兴趣。在本文中，我们提供了简单对角类型组的直径的明确界限。因此，我们获得了轨道直径小于或等于 4 的简单对角群的分类。作为其中的一部分，我们对覆盖数和共轭宽度最多为 3 的所有有限单群进行分类。我们还证明了覆盖李型群的数目和共轭宽度。