The Local Subgroups of the Fischer Groups
The Local Subgroups of the Fischer Groups
复制标题
费舍尔群的局部子群
DOI：
10.1112/jlms/s2-36.1.77
复制
发表时间：
1987
影响因子：
1.2
通讯作者：
R. Wilson
中科院分区：
文献类型：
--
作者：
R. Wilson
本文确定了散发单群Fi 23（p= 3）和Fi 24（p= 2和3）的极大/Mocal子群，以及Fia 4（p= 2和3）的自同构群Fi 24 ^ F124：2的极大/Mocal子群. Flaass [2]确定了Fi 22和Fi 23的2-局部子群，[8]给出了Fi 22的3-局部子群。由于p^ 5的p-局部子群很容易确定，这就完成了Fischer群的极大p-\oca\子群的分类。事实上，所有有限单群的所有局部极大子群现在都是已知的，除了Monster和Baby Monster的2-局部子群（见[3]）。首先利用[10]和[11]的技巧确定群Fi 23，Fi 24和Fi 24的极大3-局部子群。然后，我们对该方法进行了改进，使之能对Fi 24和Fi 24的2-局部子群进行分类（比较[4]的方法）。我们的符号遵循ATLAS [I]。
In this paper we determine the maximal/Mocal subgroups of the sporadic simple groups Fi23 (for p= 3) and Fi24 (for p= 2 and 3), and of the automorphism group Fi24^ F124: 2 of Fia4 (for p= 2 and 3). The 2-local subgroups of Fi22 and Fi23 have been determined by Flaass [2], and the 3-local subgroups of Fi22 are given in [8]. Since the/j-local subgroups for p^ 5 are easy to determine, this completes the classification of the maximal p-\oca\subgroups of the Fischer groups. Indeed, all local maximal subgroups of all finite simple groups are now known, with the exception of the 2-local subgroups of the Monster and the Baby Monster (see [3]). First we use the techniques of [10] and [11] to determine the maximal 3-local subgroups of the groups Fi23, Fi24 and Fi24. Then we modify the method to classify the 2-local subgroups of Fi24 and Fi24 (compare the methods of [4]). Our notation follows the ATLAS [I].