发表机构
Institute for Mathematical Sciences, Renmin University of China; Laboratory of Mathematics and Complex Systems (Ministry of Education), School of Mathematical Sciences, Beijing Normal University; School of Mathematics and Statistics The University of Melbourne（中国人民大学数学科学研究所; 北京师范大学数学科学学院数学与复杂系统教育部重点实验室; 墨尔本大学数学与统计学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文确定了几乎单群上具有正规连接集的连通Cayley图的完全自同构群，并刻画其生成条件，推广了错排图等结果，还建立了图双正则表示的标准并纠正了交错群的结论。
AI 中文摘要
我们确定了每个具有正规连接集的几乎单群上的连通Cayley图的完全自同构群。我们还精确刻画了完全自同构群何时由右平移、保持连接集的群自同构以及逆映射生成。我们的结果实质上推广了文献中的若干结果，包括对错排图、完全转置图和完全交错群图的已知自同构群确定。作为进一步应用，我们建立了有限非交换单群承认图双正则表示的标准，并精确确定了哪些交错群承认该表示，纠正了文献中的论断。
英文摘要
We determine the full automorphism group of every connected Cayley graph on an almost simple group with a normal connection set. We also characterize exactly when the full automorphism group is generated by right translations, group automorphisms preserving the connection set, and inversion. Our results substantially generalize several results in the literature, including the known determinations of the automorphism groups of derangement graphs, complete transposition graphs and complete alternating group graphs. As a further application, we establish criteria for a finite nonabelian simple group to admit a graphical doubly regular representation and determine exactly which alternating groups do so, correcting claims in the literature.
