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Proceedings of the London Mathematical Society Advance Access originally published online on March 21, 2008
Proceedings of the London Mathematical Society 2008 97(1):239-271; doi:10.1112/plms/pdm057
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© 2008 London Mathematical Society

Normal subsystems of fusion systems

Michael Aschbacher

California Institute of Technology
Pasadena, CA 91125
USA

Received 14 November 2006. Revision received 16 August 2007.

The notion of a fusion system was first defined and explored by Puig in the context of modular representation theory. Later, Broto, Levi, and Oliver significantly extended the theory of fusion systems as a tool in homotopy theory. In this paper we begin a program to establish a local theory of fusion systems similar to the local theory of finite groups. In particular, we define the notion of a normal subsystem of a saturated fusion system, and prove some basic results about normal subsystems and factor systems.

This work was partially supported by NSF-0504852.

2000 Mathematics Subject Classification 20D20, 55R35.


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