A characterization of the 2-fusion system of L_4(q)
A characterization of the 2-fusion system of L_4(q)
复制标题
L_4(q) 2-融合系统的表征
DOI：
10.1112/blms/bdu083
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
J. Lynd
中科院分区：
文献类型：
--
作者：
J. Lynd
本文研究了有限2-群S上的饱和融合系统F，该系统具有基于二面体2-群的Baumann分支。设F是2-完全的，不含非平凡正规2-子群，且分支的中心化子是循环2-群，证明了F是L4（q1）的2-fusion系，其中q1 = 3（mod 4）.这应该被看作是对M.阿施巴赫在素数2时对简单聚变系统的分类。有限单群分类的分量类型部分中的相应问题（L_2（q），A_7标准形式问题）是最后完成的问题之一，并且最终仅在具有重型火炮的归纳上下文中得到解决。主要是由于要求组件是鲍曼，我们的主要论点相比之下，只需要2融合分析和转移。在群范畴中我们推出了一个相应的结果。
We study a saturated fusion system F on a finite 2-group S having a Baumann component based on a dihedral 2-group. Assuming F is 2-perfect with no nontrivial normal 2-subgroups, and the centralizer of the component is a cyclic 2-group, it is shown that F is uniquely determined as the 2-fusion system of L_4(q_1) for some q_1 = 3 (mod 4). This should be viewed as a contribution to a program recently outlined by M. Aschbacher for the classification of simple fusion systems at the prime 2. The corresponding problem in the component-type portion of the classification of finite simple groups (the L_2(q), A_7 standard form problem) was one of the last to be completed, and was ultimately only resolved in an inductive context with heavy artillery. Thanks primarily to requiring the component to be Baumann, our main arguments by contrast require only 2-fusion analysis and transfer. We deduce a companion result in the category of groups.