Fusion systems and localities

2013/01/01 by Andrew Chermak · 12 citations
Mathematics · #Finite Group Theory Research #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.1007/s11511-013-0099-5

Abstract

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

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• Evaluation maps and transfers for free loop spaces II
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