论文标题
关于双固定可分离性和Wilson-Zalesskii物业
On double coset separability and the Wilson-Zalesskii property
论文作者
论文摘要
如果所有有限生成的子组$ h，k \ leqslant g $，一个有限有限的$ g $具有Wilson-Zalesskii属性，一个具有$ \ bar {h} \ cap \ cap \ bar {k} = \ edmectlline {h \ cap k} $，在$ $ $ g中，$ g。该属性在几篇论文中发挥了重要作用，通常与双框的可分离性结合在一起。在本说明中，我们表明Wilson-Zalesskii属性实际上是每个可分开的群体所享有的。我们还构建了一个不可分离且没有Wilson-Zalesskii属性的LERF组的示例。
A residually finite group $G$ has the Wilson-Zalesskii property if for all finitely generated subgroups $H,K \leqslant G$, one has $\bar{H} \cap \bar{K}=\overline{H \cap K}$, where the closures are taken in the profinite completion $\widehat G$ of $G$. This property played an important role in several papers, and is usually combined with separability of double cosets. In the present note we show that the Wilson-Zalesskii property is actually enjoyed by every double coset separable group. We also construct an example of a LERF group that is not double coset separable and does not have the Wilson-Zalesskii property.
