On double coset separability and the Wilson-Zalesskii property

Minasyan, Ashot (2023) On double coset separability and the Wilson-Zalesskii property. Bulletin of the London Mathematical Society, 55 (2), 1033-1040. (doi:10.1112/blms.12775).

Record type: Article

Abstract

A residually finite group (Formula presented.) has the Wilson–Zalesskii property if for all finitely generated subgroups (Formula presented.), one has (Formula presented.), where the closures are taken in the profinite completion (Formula presented.) of (Formula presented.). 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 an subgroup separable (LERF) group that is not double coset separable and does not have the Wilson–Zalesskii property.

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Accepted/In Press date: 1 November 2022

e-pub ahead of print date: 4 January 2023

Published date: 4 April 2023

Additional Information: Funding Information: I am grateful to Pavel Zalesskii for fruitful discussions and for drawing my attention to the paper [2], which motivated this note. Publisher Copyright: © 2023 The Authors. Bulletin of the London Mathematical Society is copyright © London Mathematical Society.