AI 中文总结
该研究证明了阶不超过8的域上李型有限单群存在平方为整个群的共轭类，结合此前结果完成汤普森猜想的证明，还明确构造相关类并提供计算证书。
AI 中文摘要
我们证明，每个阶不超过8的域上的李型有限单群都包含一个共轭类，其平方等于整个群。结合先前已证明的情形，我们的结果完成了汤普森猜想的证明。我们明确构造了所需的类，处理了所有低秩识别问题，并提供了用于例外特征计算的精确计算证书。
英文摘要
We prove that every finite simple group of Lie type over a field of order at most 8 contains a conjugacy class whose square is the whole group. Together with the previously established cases, our results complete the proof of Thompson's conjecture. We explicitly construct the required class, address all low-rank identifications, and provide the precise computational certificates used in the exceptional character calculations.
Comments69 pages. Comments welcome!
