Fusion systems and localities

Andrew Chermak Mathematics Department, Kansas State University

Group Theory and Lie Theory mathscidoc:1701.17001

Acta Mathematica, 211, (1), 47-139, 2011.8
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.
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@inproceedings{andrew2011fusion,
  title={Fusion systems and localities},
  author={Andrew Chermak},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203401404371776},
  booktitle={Acta Mathematica},
  volume={211},
  number={1},
  pages={47-139},
  year={2011},
}
Andrew Chermak. Fusion systems and localities. 2011. Vol. 211. In Acta Mathematica. pp.47-139. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203401404371776.
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