Meierfrankenfeld纲领的局部方法：初始设定与对称情形
A local approach to a programme of Meierfrankenfeld: initial setting and the symmetric case
- RPTU University Kaiserslautern-Landau（凯泽斯劳滕-兰道理工大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文在融合系统与局部性框架下推广Meierfrankenfeld等人的大p-子群局部结构理论，建立初始设定并处理对称情形，为后续研究奠定基础。
AI中文摘要：
群$G$的一个大$p$-子群是指$G$的一个自中心化$p$-子群$Q \le G$，其正规化子控制$Q$的所有非平凡中心子群的正规化子。2016年，Meierfrankenfeld、Stellmacher和Stroth证明了描述具有大$p$-子群的有限群的$p$-局部结构的结果（主要例子来自定义特征为$p$的有限李型群）。该结果是在研究局部特征为$p$的群的更广泛框架内的一项重大成功。我们试图为融合系统和局部性（locality）产生一个类似于Meierfrankenfeld、Stellmacher和Stroth的结果。Ellen Henke和作者先前的工作表明，合理的推广可以在融合系统领域或局部性世界中等价地表述和解决。特别地，在本文中我们为分析奠定基础，展示了在局部性中工作带来的明显优势：它允许遵循与群情形相同的推理路线。因此，我们产生了类似于Meierfrankenfeld等人2016年结果中的约化结果和情形细分，并按照类比进行，处理某些自然正交模的出现以及需要研究的第一个情形，即所谓的对称情形。其余情形将出现在未来的出版物中。
英文摘要：
A large $p$-subgroup of a group $G$ is a self-centralizing $p$-subgroup $Q \le G$ whose normalizer controls the normalizers of all the non-trivial, central subgroups of $Q$. In 2016 Meierfrankenfeld, Stellmacher and Stroth produced a result describing the $p$-local structure of a finite group having a large $p$-subgroup (the main examples arising from finite groups of Lie type in defining characteristic $p$). This result is a major success within the wider framework of studying groups of local characteristic $p$. We attempt to produce a result analogous to that of Meierfrankenfeld, Stellmacher and Stroth, but for fusion systems and localities. Previous work of Ellen Henke and the author shows that reasonable generalizations can be formulated and solved equivalently either within the realm of fusion systems or in the world of localities. In particular, in the present paper we set the stage for our analysis, showing how working within a locality grants a clear advantage: it allows to follow the same lines of reasoning as for a group. We therefore produce analogous reduction results and case subdivision as those in the 2016 result of Meierfrankenfeld et al. and, proceeding according to the analogy, we deal with occurrences of certain natural orthogonal modules and with the first of the cases that are to be studied, the so-called symmetric case. The remaining cases will appear in future publications.
