Memoirs of the American Mathematical Society 2011; 110 pp; softcover Volume: 209 ISBN10: 0821853031 ISBN13: 9780821853030 List Price: US$74 Individual Members: US$44.40 Institutional Members: US$59.20 Order Code: MEMO/209/986
 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 Lbalance theorem of Gorenstein and Walter for fusion systems. He defines a notion of composition series and composition factors and proves a JordonHölder theorem for fusion systems. Table of Contents  Introduction
 Background
 Direct products
 \(\mathcal {E}_{1}\wedge \mathcal {E}_{2}\)
 The product of strongly closed subgroups
 Pairs of commuting strongly closed subgroups
 Centralizers
 Characteristic and subnormal subsystems
 \(T\mathcal {F}_{0}\)
 Components
 Balance
 The fundamental group of \(\mathcal{F}^{c}\)
 Factorizing morphisms
 Composition series
 Constrained systems
 Solvable fusion systems
 Fusion systems in simple groups
 An example
 Bibliography
