Acta Mathematica

Fusion systems and localities

Andrew Chermak

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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.

Article information

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

Dates
Received: 26 August 2011
Revised: 15 January 2013
First available in Project Euclid: 31 January 2017

Permanent link to this document
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
2013 © Institut Mittag-Leffler

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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