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The generalized Fitting subsystem of a fusion system
About this Title
Michael Aschbacher, California Institute of Technology, Pasadena, California 91125
Publication: Memoirs of the American Mathematical Society
Publication Year:
2011; Volume 209, Number 986
ISBNs: 978-0-8218-5303-0 (print); 978-1-4704-0600-4 (online)
DOI: https://doi.org/10.1090/S0065-9266-2010-00621-5
Published electronically: July 21, 2010
MSC: Primary 20D20, 55R35
Table of Contents
Chapters
- Introduction
- 1. Background
- 2. Direct products
- 3. $\mathcal {E}_{1}\wedge \mathcal {E}_{2}$
- 4. The product of strongly closed subgroups
- 5. Pairs of commuting strongly closed subgroups
- 6. Centralizers
- 7. Characteristic and subnormal subsystems
- 8. $T\mathcal {F}_{0}$
- 9. Components
- 10. Balance
- 11. The fundamental group of $\mathcal {F}^{c}$
- 12. Factorizing morphisms
- 13. Composition series
- 14. Constrained systems
- 15. Solvable fusion systems
- 16. Fusion systems in simple groups
- 17. An example
Abstract
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 extended the theory and used it as a tool in homotopy theory. We seek to build a local theory of fusion systems, analogous to the local theory of finite groups, involving normal subsystems and factor systems. Among other results, we define the notion of a simple system, the generalized Fitting subsystem of a fusion system, and prove the L-balance theorem of Gorenstein and Walter for fusion systems. We define a notion of composition series and composition factors, and prove a Jordon-Hölder theorem for fusion systems.- Michael Aschbacher, Normal subsystems of fusion systems, Proc. Lond. Math. Soc. (3) 97 (2008), no. 1, 239–271. MR 2434097, DOI 10.1112/plms/pdm057
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