Acta Mathematica

Fusion systems and localities

Andrew Chermak

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

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

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2013 © Institut Mittag-Leffler


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

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