Fusion systems and localities

• 成果类型: Article
• 署名作者: Chermak, Andrew
• 署名单位: Kansas State University
• 刊物名称: ACTA MATHEMATICA
• ISSN/ISSBN: 0001-5962
• DOI: 10.1007/s11511-013-0099-5
• 发表日期: 2013
• 页码: 47-139
• 关键词: replacement theorem; p(g

摘要

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 -localities of Puig are examples, as are groups in the ordinary sense. As an application we show that if is a saturated fusion system over a finite p-group then there exists a centric linking system having as its fusion system, and that 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.