Reductions to simple fusion systems
Reductions to simple fusion systems
复制标题
简化为简单的融合系统
DOI：
10.1112/blms/bdw052
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发表时间：
2016
影响因子：
0.9
通讯作者：
B. Oliver
中科院分区：
文献类型：
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作者：
B. Oliver
我们证明了如果E <$F是p-群T <$S上的饱和融合系统，使得CS（E）<$T，并且AutF（T）/AutE（T）或Out（E）是p-可解的，那么F可以通过交替取p-幂指数或指数素数为p的正规子系统而“约化”为E。特别地，当E是单群并且被已知单群K“驯服地实现”时，情况就是这样。这回答了Michael Aschbacher提出的一个问题，并且在分析简单融合系统中的对合中心化子时很有用，与他通过对某些2-融合系统进行分类来重新证明有限单群的部分分类的程序有关。
We prove that if E⊴F are saturated fusion systems over p ‐groups T⊴S , such that CS(E)⩽T , and either AutF(T)/AutE(T) or Out(E) is p ‐solvable, then F can be ‘reduced’ to E by alternately taking normal subsystems of p ‐power index or of index prime to p . In particular, this is the case whenever E is simple and ‘tamely realized’ by a known simple group K . This answers a question posed by Michael Aschbacher, and is useful when analyzing involution centralizers in simple fusion systems, in connection with his program for reproving parts of the classification of finite simple groups by classifying certain 2‐fusion systems.