融合系统和场所中的一些产品
Some products in fusion systems and localities
摘要：
饱和融合系统的理论在许多方面类似于有限群的理论。然而，有限群理论中的一些概念很难转化为融合系统。例如，正常子系统与其他子系统的乘积仅在特殊情况下定义。本文利用局部域理论证明了如下结果：设$\mathcal{F}$是$p$ -群$S$上的饱和融合系统.如果$\mathcal{E}$是$\mathcal{F}$在$T\leq S$上的正常子系统，$\mathcal{D}$是$N_{\mathcal{F}}(T)$在$R\leq S$上的次正常子系统，则存在$\mathcal{F}$在$TR$上的次正常子系统$\mathcal{E}\mathcal{D}$，其在$\mathcal{F}$中扮演$\mathcal{E}$和$\mathcal{D}$的产物的角色。如果$N_{\mathcal{F}}(T)$中$\mathcal{D}$正常，则$\mathcal{E}\mathcal{D}$在$\mathcal{F}$中正常。它示出的方式，子系统$\mathcal{E}\mathcal{D}$是密切相关的自然产生的产品在某些地方连接到$\mathcal{F}$。
英文摘要：
The theory of saturated fusion systems resembles in many parts the theory of finite groups. However, some concepts from finite group theory are difficult to translate to fusion systems. For example, products of normal subsystems with other subsystems are only defined in special cases. In this paper the theory of localities is used to prove the following result: Suppose $\mathcal{F}$ is a saturated fusion system over a $p$-group $S$. If $\mathcal{E}$ is a normal subsystem of $\mathcal{F}$ over $T\leq S$, and $\mathcal{D}$ is a subnormal subsystem of $N_{\mathcal{F}}(T)$ over $R\leq S$, then there is a subnormal subsystem $\mathcal{E}\mathcal{D}$ of $\mathcal{F}$ over $TR$, which plays the role of a product of $\mathcal{E}$ and $\mathcal{D}$ in $\mathcal{F}$. If $\mathcal{D}$ is normal in $N_{\mathcal{F}}(T)$, then $\mathcal{E}\mathcal{D}$ is normal in $\mathcal{F}$. It is shown along the way that the subsystem $\mathcal{E}\mathcal{D}$ is closely related to a naturally arising product in certain localities attached to $\mathcal{F}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
