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Saturated fusion systems over $ 2$-groups


Authors: Bob Oliver and Joana Ventura
Journal: Trans. Amer. Math. Soc. 361 (2009), 6661-6728
MSC (2000): Primary 20D20; Secondary 20D45, 20D08
DOI: https://doi.org/10.1090/S0002-9947-09-04881-8
Published electronically: July 21, 2009
MathSciNet review: 2538610
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Abstract: We develop methods for listing, for a given 2-group $ S$, all nonconstrained centerfree saturated fusion systems over $ S$. These are the saturated fusion systems which could, potentially, include minimal examples of exotic fusion systems: fusion systems not arising from any finite group. To test our methods, we carry out this program over four concrete examples: two of order $ 2^7$ and two of order $ 2^{10}$. Our long term goal is to make a wider, more systematic search for exotic fusion systems over 2-groups of small order.


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Additional Information

Bob Oliver
Affiliation: Laboratoire d’analyse, géométrie et applications, Institut Galilée, Av. J-B Clément, 93430 Villetaneuse, France
Email: bobol@math.univ-paris13.fr

Joana Ventura
Affiliation: Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1049–001 Lisboa, Portugal
Email: jventura@math.ist.utl.pt

DOI: https://doi.org/10.1090/S0002-9947-09-04881-8
Keywords: Finite groups, 2-groups, fusion, simple groups.
Received by editor(s): February 29, 2008
Published electronically: July 21, 2009
Additional Notes: The first author was partially supported by UMR 7539 of the CNRS
The second author was partially supported by FCT/POCTI/FEDER and grant PDCT/MAT/58497/2004.
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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