Reduced fusion systems over 2-groups of small order
Reduced fusion systems over 2-groups of small order
复制标题
减少 2 组小阶融合系统
DOI：
10.1016/j.jalgebra.2017.06.016
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
J. Ventura
中科院分区：
文献类型：
--
作者：
Kasper K. S. Andersen;B. Oliver;J. Ventura
证明了当S至多为29阶2-群时，S上的每个约化融合系统是有限单群的融合系统，并且是驯服的。然后得出结论：在最多29阶的2-群上的每个饱和融合系统都是可实现的。关于这一结果，最有趣的是证明方法：我们证明了在这个范围内有阶的2-群中，可以是有限单群的Sylow 2-子群的群几乎完全由Bender关于具有强2-嵌入子群的群的分类的准则决定。
We prove, whenSis a 2-group of order at most 29, that each reduced fusion system overSis the fusion system of a finite simple group and is tame. It then follows that each saturated fusion system over a 2-group of order at most 29is realizable. What is most interesting about this result is the method of proof: we show that among 2-groups with order in this range, the ones which can be Sylow 2-subgroups of finite simple groups are almost completely determined by criteria based on Bender's classification of groups with strongly 2-embedded subgroups.