## Acta Mathematica

### Fusion systems and localities

Andrew Chermak

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

#### Article information

Source
Acta Math., Volume 211, Number 1 (2013), 47-139.

Dates
Revised: 15 January 2013
First available in Project Euclid: 31 January 2017

https://projecteuclid.org/euclid.acta/1485892723

Digital Object Identifier
doi:10.1007/s11511-013-0099-5

Mathematical Reviews number (MathSciNet)
MR3118305

Zentralblatt MATH identifier
1295.20021

Rights

#### Citation

Chermak, Andrew. Fusion systems and localities. Acta Math. 211 (2013), no. 1, 47--139. doi:10.1007/s11511-013-0099-5. https://projecteuclid.org/euclid.acta/1485892723

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