论文标题
嵌入到左下的简单组中
Embeddings into left-orderable simple groups
论文作者
论文摘要
我们证明，每个可计数的左定组都嵌入有限生成的左定单简单组中。此外，如果第一组具有可计算的左顺序，则简单组还具有可计算的左顺序。 我们还为带有递归枚举的正锥的左订单组获得了Boone-Higman-Thompson型定理。这些嵌入是Frattini嵌入，并且每当初始组有限地生成时，等距。 最后，我们对汤普森的定理对单词问题的定理保存将嵌入到有限生成的简单组中，并观察到嵌入是等距的。
We prove that every countable left-ordered group embeds into a finitely generated left-ordered simple group. Moreover, if the first group has a computable left-order, then the simple group also has a computable left-order. We also obtain a Boone-Higman-Thompson type theorem for left-orderable groups with recursively enumerable positive cones. These embeddings are Frattini embeddings, and isometric whenever the initial group is finitely generated. Finally, we reprove Thompson's theorem on word problem preserving embeddings into finitely generated simple groups and observe that the embedding is isometric.
