On double coset separability and the Wilson-Zalesskii property

Abstract

A residually finite group $G$ has the Wilson-Zalesskii property if for all finitely generated subgroups $H,K⩽G$, one has $\bar{H}\cap \bar{K}=\overline{H\cap K}$, where the closures are taken in the profinite completion $\hat{G}$ 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.

v2: 6 pages; this version has been accepted for publication

Cited by in corpus (1)

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