小仿射秩3图的自同构群
The automorphism groups of small affine rank 3 graphs
AI总结：
本文研究仿射秩3图的自同构群，通过确定有限多个较小图的完整自同构群并结合已知结果，将一般问题归结为基座为非交换单群的情形。
摘要：
秩3图是偶数阶秩3置换群的轨道图。尽管秩3图的分类已经完成（例如参见Brouwer和Van Maldeghem近期专著《强正则图》第11章），但这些图的全自同构群（等价地，秩3群的2-闭包）尚未被明确描述，尽管关于这一主题已有大量信息可用。在本篇注记中，我们针对仿射秩3图解决这一问题。我们求出了有限多个相对较小图的自同构群，并证明在已知结果的基础上，这提供了仿射秩3图自同构群的完整描述，从而将一般问题归结为自同构群的基座为非交换单群的情形。
英文摘要：
A rank 3 graph is an orbital graph of a rank 3 permutation group of even order. Despite the classification of rank 3 graphs being complete, see, e.g., Chapter 11 of the recent monograph 'Strongly regular graphs' by Brouwer and Van Maldeghem, the full automorphism groups of these graphs (equivalently, the 2-closures of rank 3 groups) have not been explicitly described, though a lot of information on this subject is available. In the present note, we address this problem for the affine rank 3 graphs. We find the automorphism groups for finitely many relatively small graphs and show that modulo known results, this provides the full description of the automorphism groups of the affine rank 3 graphs, thus reducing the general problem to the case when the socle of the automorphism group is nonabelian simple.
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