论文标题
地区之间同构的扩展
Extensions of homomorphisms between localities
论文作者
论文摘要
我们表明，与饱和融合系统关联的链接系统的自动形态组$ \ MATHCAL {F} $仅取决于$ \ Mathcal {f} $，只要链接系统的对象集为$ \ MATHRM {autrm {aut}（\ Mathcal {f}）$ - invariant。众所周知，这对于将奥利弗（Oliver）定义中的系统链接起来是正确的，但是我们证明了结果也适用于本文作者先前介绍的相当多的一般定义中的链接系统。事实证明，与链接系统相对应的类似组的结构，也证明了类似的结果。我们的论点是基于一个普遍的引理，该论点是关于存在区域之间同态的存在。该引理还用于抑制Chermak定理，表明在同一融合系统上的两个可能不同的链接位置的部分正常亚组之间存在自然的射击。
We show that the automorphism group of a linking system associated to a saturated fusion system $\mathcal{F}$ depends only on $\mathcal{F}$ as long as the object set of the linking system is $\mathrm{Aut}(\mathcal{F})$-invariant. This was known to be true for linking systems in Oliver's definition, but we demonstrate that the result holds also for linking systems in the considerably more general definition introduced previously by the author of this paper. A similar result is proved for linking localities, which are group-like structures corresponding to linking systems. Our argument builds on a general lemma about the existence of an extension of a homomorphism between localities. This lemma is also used to reprove a theorem of Chermak showing that there is a natural bijection between the sets of partial normal subgroups of two possibly different linking localities over the same fusion system.
