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Fusion systems


Authors: Michael Aschbacher and Bob Oliver
Journal: Bull. Amer. Math. Soc. 53 (2016), 555-615
MSC (2010): Primary 20E25; Secondary 20D05, 20D20, 20E45, 20C20, 55R35
Published electronically: June 29, 2016
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Abstract: This is a survey article on the theory of fusion systems, a relatively new area of mathematics with connections to local finite group theory, algebraic topology, and modular representation theory. We first describe the general theory and then look separately at these connections.


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Additional Information

Michael Aschbacher
Affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125
Email: asch@caltech.edu

Bob Oliver
Affiliation: Université Paris 13, Sorbonne Paris Cité, LAGA, UMR 7539 du CNRS, 99, Av. J.-B. Clément, 93430 Villetaneuse, France
Email: bobol@math.univ-paris13.fr

DOI: http://dx.doi.org/10.1090/bull/1538
Keywords: Fusion, Sylow subgroups, finite simple groups, classifying spaces, modular representation theory.
Received by editor(s): December 27, 2015
Published electronically: June 29, 2016
Additional Notes: The first author was partially supported by NSF DMS-1265587 and NSF DMS-0969009.
The second author was partially supported by UMR 7539 of the CNRS
Article copyright: © Copyright 2016 American Mathematical Society