Finite simple groups of parabolic characteristic p

实际上有两种不同的方法来修正有限单群的分类。一个是G.戈伦施泰因河里昂和R.所罗门（GLS），这将给出一个证明以下的经典路线。最近 M. Aschbacher在融合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。与之平行的是美国政府的工作。Meierfarnkenfeld，B. Stellmacher和G. Stroth（MSS）本文的主要目的是在MSS和其他两个项目的结果之间建立一个桥梁，以便它们可以在那里使用。在原来的分类中，有一个明确的细分，即组分类型组和局部特征组。GLS现在说的是偶数类型组，而不是局部特征组。特征2. Aschbacher在他的计划减少了问题考虑群体，其中当地的子群包含一个最大的交换子群的特征2。密钥可以是由于K的结果。Magaard和G. Stroth分类的群体是甚至类型，但不是抛物线特性2。为了使MSS的结果可用于GLS，证明这些结果对于抛物特征2就足够了，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，这也将使桥梁使用的结果在阿施巴赫计划。这个项目的目的是实现这一目标。更精确地说，我们将证明结构定理MSS的抛物特征群2。此外，识别出现的简单群也应该通过假设抛物线特征2来完成。特别是我们必须处理的群体$G$包含一个子群$H$的奇指数，这是一个自同构群的一组李型的特征2。仅假设抛物线特征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).