Finite simple groups of parabolic characteristic p

实际上有两种不同的方法来修正有限简单群的分类。一个是G. Gorenstein， R. Lyons和R. Solomon （GLS）他们将按照经典路线给出证明。最近，阿什巴赫在核聚变系统的帮助下开始了一种新的方法。到目前为止，后一种方法只适用于组件类型的组。与之平行的还有U. meerfarnkenfeld， B. Stellmacher和G. Stroth （MSS）的工作，他们的目标是对地方特征p的群体进行新的分类。这个项目的主要目的是在MSS的结果和其他两个项目之间建立一座桥梁，以便它们可以在那里使用。在原始分类中，组分类型组和局部特征组2有明显的细分。GLS现在说的是偶数类型的群体，而不是具有本地特征的群体。在该方案中，Aschbacher将问题简化为考虑包含极大阿贝尔子群的局部子群具有特征2的群。一个关键可能是由于K. Magaard和G. Stroth对偶数型但不具有抛物特征的群进行分类的结果2。为了使MSS的结果适用于GLS，只需证明这些结果适用于抛物型特征2，即包含Sylow 2-子群的局部子群具有局部特征2。作为一个副作用，这也为在Aschbacher程序中使用结果提供了桥梁。这个项目的目的就是要达到这个目标。更精确地，我们将证明抛物型特征2群的MSS中的结构定理。此外，确定出现的简单群也应该通过假设抛物线特性2来完成。特别地，我们必须处理含有奇数指标子群H$的群G$，它是特征二的李型群的自同构群。假设抛物线特征2，我们将确定所有这样的对（G，H）

There are actually two different approaches to revise the classification of the finite simple groups. One due to G. Gorenstein, R. Lyons and R. Solomon (GLS) which will give a proof following the classical line. Recently M. Aschbacher started a new approach with the help of fusion systems. So far the latter approach just work for the groups of component type. Parallel there is the work of U. Meierfarnkenfeld, B. Stellmacher and G. Stroth (MSS) which aim to gve a new classification of the groups of local characteristic p. The main aim of this project is bulid a bridge between the results of MSS and the other two projects such that they can be used there.In the original lassification there was a clear subdivision in groups of component type and groups of local characteristic 2.GLS now speaks of groups of even type instead of groups of local characteristic 2. Aschbacher in his program reduces the problem to consider groups in which local subgroups containing a maximal abelian subgroup are of characteristic 2. A key could be a result due to K. Magaard and G. Stroth which classifies the groups which are of even type but not of parabolic characteristic 2. To make the results of MSS accessible for GLS it would suffice to prove these results for parabolic characteristic 2, i.e. local subgroups containing a Sylow 2-subgroup are of local characteristic 2. As a side effect this would also give the bridge to use the results in the Aschbacher program.The aim of this project is to achieve exactly this goal. More precise we will prove the structure theorem in MSS for groups of parabolic characteristic 2. Furthermore identifying the simple groups showing up should also be done by just assuming parabolic characteristic 2. In particular we have to deal with groups $G$ containing a subgroup $H$ of odd index, which is an automorphism group of a group of Lie type in characteristic two. Just assuming parabolic characteristic 2 we will determine all such pairs (G,H).