费歇尔和魔群散在群的西罗3-子群上的融合系统——II
Fusion Systems on Sylow $3$-subgroups of Fischer and Monster sporadic groups -- II
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中文总结 AI 辅助
该研究对散在群$\mathrm{Fi}_{24}'$和$\mathrm{M}$的西罗3-子群上的无核融合系统进行分类，完成了奇数$p$时散在群西罗$p$-子群无核融合系统分类项目，还扩展理论并描述算法，大幅加快找$p$-群无核融合系统的过程。
中文摘要 AI 辅助
我们对散在群$\mathrm{Fi}_{24}'$和$\mathrm{M}$的西罗3-子群上的所有无核融合系统进行分类。对散在群西罗$p$-子群上所有无核融合系统进行分类的项目已开展多年，由众多作者在多篇论文中完成。我们完成了奇数$p$的该项目。在此过程中，我们扩展了原本质子群理论，并描述了使在$p$-群上找到所有无核融合系统的过程加快几个数量级的算法。
英文摘要
We classify all corefree fusion systems on a Sylow 3-subgroup of the sporadic groups $\mathrm{Fi}_{24}'$ and $\mathrm{M}$. The program to classify of all corefree fusion systems on Sylow $p$-subgroups of sporadic groups has been running for many years, comprising of work done in several papers by numerous authors. We complete this program for $p$ odd. In the process, we expand the theory of proto-essential subgroups and describe algorithms that make the process of finding all corefree fusion systems on a $p$-group better by several orders of magnitude.
