Fusion systems and localities
Fusion systems and localities
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融合系统和地点
DOI：
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发表时间：
2013
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通讯作者：
A. Chermak
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文献类型：
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作者：
A. Chermak
我们引入了客观偏群，其中Broto，Levi和Oliver的链系和p-局部有限群，Oliver和Ventura的转运子系统，以及Puig的$F-位置是例子，通常意义下的群也是这样。作为应用，我们证明了：如果$${数学{F}}$$F是有限p-群上的饱和融合系统，则存在以$$\数学{F}}$$F为融合系统的中心联结系统$${\数学{L}}$L，并且${\数学{L}}$$L在同构之前是唯一的。证明依赖于对有限单群的间接分类，并且由于这个原因，也许最终是可去除的。
We introduce objective partial groups, of which the linking systems and p-local finite groups of Broto, Levi, and Oliver, the transporter systems of Oliver and Ventura, and the $${\mathcal{F}}$$F-localities of Puig are examples, as are groups in the ordinary sense. As an application we show that if $${\mathcal{F}}$$F is a saturated fusion system over a finite p-group then there exists a centric linking system $${\mathcal{L}}$$L having $${\mathcal{F}}$$F as its fusion system, and that $${\mathcal{L}}$$L is unique up to isomorphism. The proof relies on the classification of the finite simple groups in an indirect and—for that reason—perhaps ultimately removable way.