关于对角型群的轨道直径
On the Orbital Diameter of Groups of Diagonal Type
摘要：
本原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。本文给出了简单对角型群的直径的明确界。作为结果，我们得到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，我们对所有具有覆盖数且共轭宽度不超过3的有限单群进行了分类。我们还证明了李型群的覆盖数和共轭宽度的一般界。
英文摘要：
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.
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