论文标题
扭曲的Brin-Thompson组
Twisted Brin-Thompson groups
论文作者
论文摘要
我们构建了一个无限简单的团体家庭，我们称为\ emph {扭曲的Brin-Thompson群体}，概括了Brin的高维汤普森组$ sv $（$ s \ in \ mathbb {n} $）。我们使用扭曲的Brin-Thompson组来证明有关简单组的各种结果。例如，我们证明，每个有限生成的组都将准静态嵌入为两生简单组的亚组，从而增强了布里森的结果。我们还制作了一个简单组的示例，这些示例包含每$ sv $，以及每个直角artin组，包括$ \ textrm {f} _ \ infty $的示例，以及类型$ \ textrm {f} _ {n-1} _ {n-1} $的类型的示例，但不是$ \ \ textrm {f textrm {f} $ n $ n $ n $ n $ n usitary norary norary norary norary norary norary n usitary norary norary norary norary norary。这提供了第二个已知的无限群体，这些家族以其有限性特性为特色。
We construct a family of infinite simple groups that we call \emph{twisted Brin-Thompson groups}, generalizing Brin's higher-dimensional Thompson groups $sV$ ($s\in\mathbb{N}$). We use twisted Brin-Thompson groups to prove a variety of results regarding simple groups. For example, we prove that every finitely generated group embeds quasi-isometrically as a subgroup of a two-generated simple group, strengthening a result of Bridson. We also produce examples of simple groups that contain every $sV$ and hence every right-angled Artin group, including examples of type $\textrm{F}_\infty$ and a family of examples of type $\textrm{F}_{n-1}$ but not of type $\textrm{F}_n$, for arbitrary $n\in\mathbb{N}$. This provides the second known infinite family of simple groups distinguished by their finiteness properties.
