具有一般自同构群的希尔伯特空间

Coherent extension of partial automorphisms, free amalgamation, and automorphism groups

We give strengthened versions of the Herwig-Lascar and Hodkinson-Otto extension theorems for partial automorphisms of finite structures. Such strengthenings yield several combinatorial and group-theoretic consequences for homogeneous structures. For instance, we establish a coherent form of the extension property for partial automorphisms for certain Fraisse classes. We deduce from these results that the isometry group of the rational Urysohn space, the automorphism group of the Fraisse limit of any Fraisse class that is the class of all $\mathcal{F}$-free structures (in the Herwig--Lascar sen…

Definably simple stable groups with finitary groups of automorphisms

We prove that infinite definably simple locally finite groups of finite centraliser dimension are simple groups of Lie type over locally finite fields. Then, we identify conditions on automorphisms of a stable group that make it resemble the Frobenius maps, and allow us to classify definably simple stable groups in the specific case when they admit such automorphisms.

有序置换群的外自同构群

Outer Automorphism Groups of Ordered Permutation Groups

一个无限线性序集（S，<=）称为双齐次的，如果它的自同构群A（S）作用在它上面2-传递.我们证明了对于某个双齐次链（S，<=），任何群G都是自同构群A（S）的外自同构群G cong Out（A（S））.

Automorphism groups of universal diversities

We prove that the automorphism group of the Urysohn diversity is a universal Polish group. Furthermore we show that the automorphism group of the rational Urysohn diversity has ample generics, a dense conjugacy class and that it embeds densely into the automorphism group of the (full) Urysohn diversity. It follows that this latter group also has a dense conjugacy class.

一个群的自同构塔有多高？

How Tall is the Automorphism Tower of a Group?

通过计算群的自同构群、THAT群的自同构群等，迭代translation，得到群的自同构塔。每一组映射到下一个使用内自同构和一个采取直接限制在极限阶段。问题是这个过程是否终止于一个不动点，一个由自然映射同构于它的自同构群的群。在这个演讲中，我将证明每个群都有终止自同构塔。在这之后，我将讨论一个群的自同构塔的高度的集合论方面，并概述我最近与西蒙·托马斯一起证明的一个群的自同构塔被强迫而被广泛修改是一致的;事实上，在集合论的各种模型中，这个群的自同构塔几乎可以任意指定。

每个群都有一个终止的超限自同构塔

Every group has a terminating transfinite automorphism tower

一个群的自同构塔是通过计算它的自同构群、THAT群的自同构群等，迭代translation得到的。每个群使用内自同构规范地映射到下一个群，因此在极限阶段可以取直接极限并继续迭代。如果到达一个不动点，也就是说，如果到达一个由自然映射同构于它的自同构群的群，则称塔终止。如果到达一个完全群，即一个无中心且只有内自同构的群，就会发生这种情况。Wielandt [1939]证明了无中心有限群的自同构塔终止于n阶的经典结果。Rae和Roseblade [1970]证明了任何无中心Cernikov群的自同构塔终止于1000步。Hulse [1970]证明了任何无中心多环群的自同构塔终止于可数个步骤。Simon Thomas [1985]证明了任何无中心群的自同构塔最终终止。本文去掉了无中心假设，证明了每个群都有一个终止的超限自同构塔。

具有泛自同构群的Fraïssé结构

Fraïssé Structures with Universal Automorphism Groups

我们证明了具有平稳独立性的Fraïssé结构M的自同构群对于M的子结构的自同构群类是泛有的。此外，我们表明，这适用于某些齐次n-dot。

Homogeneous structures with non-universal automorphism groups

We present three examples of countable homogeneous structures (also called Fraisse limits) whose automorphism groups are not universal, namely, fail to contain isomorphic copies of all automorphism groups of their substructures. Our first example is a particular case of a rather general construction on Fraisse classes, which we call diversification, leading to automorphism groups containing copies of all finite groups. Our second example is a special case of another general construction on Fraisse classes, the mixed sums, leading to a Fraisse class with all finite symmetric groups appearing as…

序阿贝尔群的自同构群的刻划

Characterizing automorphism groups of ordered abelian groups

刻画了与序阿贝尔群的全自同构群同构的群。结果将遵循从经典定理的序群添加一个参数，从证明用于实现环作为自同态环的阿贝尔群。