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. The author seeks 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, he defines 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. He defines a notion of composition series and composition factors and proves a Jordon-Hoelder theorem for fusion systems.|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. The author seeks 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, he defines 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. He defines a notion of composition series and composition factors and proves a Jordon-Hoelder theorem for fusion systems.
- ISBN13 9780821853030
- Publish Date 20 December 2011
- Publish Status Active
- Publish Country US
- Imprint American Mathematical Society
- Format Paperback
- Pages 110
- Language English