有限单群的元素阶识别问题已被解决
The problem of recognition of finite simple groups by element orders is solved
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中文总结 AI 辅助
该研究明确了有限群元素阶识别问题的判定标准，即已知对应同构群数量且有限时可列出全部群，最终完成了所有有限单群的元素阶识别问题的求解工作。
中文摘要 AI 辅助
对于有限群$G$，设$ω(G)$为$G$的元素阶集合，$h(G)$为满足$ω(H)=ω(G)$的两两不同构的有限群$H$的数量。若$h(G)$的数值已知，且当$h(G)$有限时能列出所有满足$ω(H)=ω(G)$的有限群$H$，则称$G$的识别问题已解决。我们完成了所有有限单群识别问题的求解。
英文摘要
For a finite group $G$, let $ω(G)$ be the set of element orders of $G$ and let $h(G)$ be the number of pairwise nonisomorphic finite groups $H$ with $ω(H)=ω(G)$. We say that the recognition problem is solved for $G$ if the number $h(G)$ is known, and if it is finite, then all finite groups $H$ with $ω(H)=ω(G)$ are listed. We complete the solution of the recognition problem for all finite simple groups.
