论文标题
扭曲的Brin-Thompson群体的味道
A taste of twisted Brin-Thompson groups
论文作者
论文摘要
该注释是扭曲的Brin-Thompson团体的简短且对读者友好的介绍，该小组最近由Belk和作者建造，为一个简单的团体提供了各种有趣的属性。最值得注意的是，扭曲的Brin-Thompson组可用于证明每个有限生成的Quasi Imetricter嵌入作为有限生成的简单组的亚组。另一个重要的应用是具有任意有限长度的简单群体家族的具体构造。除了对小组和这些应用提供简洁的介绍之外，我们还在这里证明了原始论文的结果之一。也就是说，我们证明，任何有限地提出的群体忠实地表现出忠实地行动，并在一个有限生成的有限子集的稳定器上均嵌入有限的简单组中。我们认为，这可能会导致未来在解决某些群体的Boone-Higman猜想方面的进展。
This note serves as a short and reader-friendly introduction to twisted Brin-Thompson groups, which were recently constructed by Belk and the author to provide a family of simple groups with a variety of interesting properties. Most notably, twisted Brin-Thompson groups can be used to show that every finitely generated group quasi-isometrically embeds as a subgroup of a finitely generated simple group. Another important application is a concrete construction of a family of simple groups with arbitrary finiteness length. In addition to giving a concise introduction to the groups and these applications, we also prove here a strengthening of one of the results from the original paper. Namely, we prove that any finitely presented group acting faithfully and oligomorphically on a set, with finitely generated stabilizers of finite subsets, embeds in a finitely presented simple group. We believe this could potentially lead to future progress on resolving the Boone-Higman Conjecture for certain groups.
