融合系统的Krull-Remak-Schmidt定理
A Krull-Remak-Schmidt theorem for fusion systems
摘要：
我们证明了一个饱和的融合系统的分解在一个离散的$p$ -toral群作为一个产品的不可分解的子系统是唯一的正常的自同构的融合系统和置换的因素。特别地，如果融合系统有平凡中心，或者如果它的焦点子群是整个Sylow群，那么这个因子分解是唯一的（直到因子的排序）。这一结果的动机是融合系统的产品的自同构群的问题。
英文摘要：
We prove that the factorization of a saturated fusion system over a discrete $p$-toral group as a product of indecomposable subsystems is unique up to normal automorphisms of the fusion system and permutations of the factors. In particular, if the fusion system has trivial center, or if its focal subgroup is the entire Sylow group, then this factorization is unique (up to the ordering of the factors). This result was motivated by questions about automorphism groups of products of fusion systems.
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。
