The Generalized Fitting Subsystem of a Fusion System
The Generalized Fitting Subsystem of a Fusion System
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DOI：
10.1090/s0065-9266-2010-00621-5
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发表时间：
2011-02
期刊：
影响因子：
--
通讯作者：
M. Aschbacher
中科院分区：
文献类型：
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作者：
M. Aschbacher
融合系统的概念首先由普伊格在模块化表示理论的背景下定义和探索。后来，Broto，Levi和奥利弗扩展了这个理论，并将其作为同伦理论的工具。作者试图建立一个融合系统的局部理论，类似于有限群的局部理论，包括正规子系统和因子系统。在其他成果中，他定义了一个简单系统的概念，融合系统的广义拟合子系统，并证明了Gorenstein和Walter融合系统的L-平衡定理。他定义了一个概念的组成系列和组成因素，并证明了乔丹持有定理融合系统。|融合系统的概念首先由普伊格在模块化表示理论的背景下定义和探索。后来，Broto，Levi和奥利弗扩展了这个理论，并将其作为同伦理论的工具。作者试图建立一个融合系统的局部理论，类似于有限群的局部理论，包括正规子系统和因子系统。在其他成果中，他定义了一个简单系统的概念，融合系统的广义拟合子系统，并证明了Gorenstein和Walter融合系统的L-平衡定理。他定义了一个概念的组成系列和组成因素，并证明了乔丹持有定理融合系统。
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-Holder 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-Holder theorem for fusion systems.