定义特征为2的有限李型群的可除图的分量
Components of the Divisibility Graph of Finite Groups of Lie Type in Defining Characteristic $2$
AI总结：
该研究扩展前人关于奇定义特征有限李型群可除图的结果，确定了定义特征为2的有限李型群可除图的连通分量，还证明弗罗贝尼乌斯群可除图恰有两个分量。
AI中文摘要：
我们确定了若干族定义特征为2的有限李型群的可除图的连通分量，扩展了Abdolghafourian、Iranmanesh和Niemeyer（arXiv:1612.04410）的结果，该文研究的是奇定义特征。我们证明存在一个包含所有非单位幂幺类大小的特殊分量，其余每个分量要么是孤立顶点，要么是明确描述的两顶点分量；还确定了特殊分量外的孤立顶点。此外，我们在附录A中证明，弗罗贝尼乌斯群的可除图恰好有两个分量。
英文摘要：
We determine the connected components of the divisibility graph of several families of finite groups of Lie type in defining characteristic $2$, extending the result of Abdolghafourian, Iranmanesh, and Niemeyer (arXiv:1612.04410), who treated odd defining characteristic. We show that there is a distinguished component containing all nonidentity unipotent class sizes and that every other component is either an isolated vertex or an explicitly described two-vertex component. We also determine the isolated vertices outside the distinguished component. Additionally, we prove in Appendix A that the divisibility graph of a Frobenius group has exactly two components.
