AI 中文总结
本文找到怪兽群未公开的极大子群59:29的显式生成元，修正了前人关于怪兽群不存在子群PSL2(59)的结论。
AI 中文摘要
怪兽群的极大子群分类近期已完成，除极大子群59:29外，其余各极大子群的显式生成元（在共轭意义下）已通过软件mmgroup公开，相关研究见Dietrich等人（Adv. Math., 2025; J Algebra, 2026）。本文提供该最后一个极大子群的显式生成元，并阐述找到它们所开展的大量搜索工作。本文方法与Bray等人（London Math. Soc. J. Comput. Math., 2016）构造小怪兽群中47:23的方法类似，但复杂度显著更高。该结果使我们能给出怪兽群不存在子群PSL2(59)的新简捷证明，修正了Holmes与Wilson（J. London Math. Soc., 2004）的相关结论。
英文摘要
The classification of the maximal subgroups of the Monster group has been completed recently, and explicit generators for each such subgroup (up to conjugacy) have been made available for the software mmgroup, with the exception of the maximal subgroup 59:29, see Dietrich et al. (Adv. Math., 2025; J Algebra, 2026). We provide explicit generators for this last maximal subgroup and comment on the extensive search that led to finding them. Our method is similar to, but significantly more involved than Bray et al.'s (London Math. Soc. J. Comput. Math., 2016) approach for constructing 47:23 in the Baby Monster. Our result allows us to provide a new short proof that the Monster does not have a subgroup PSL2(59), correcting a result of Holmes and Wilson (J. London Math. Soc., 2004).
