On double coset separability and the Wilson-Zalesskii property
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866914767277391872 |
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| author | Minasyan, Ashot |
| author_facet | Minasyan, Ashot |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_04058 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On double coset separability and the Wilson-Zalesskii property Minasyan, Ashot Group Theory 20E26, 20E18 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. |
| title | On double coset separability and the Wilson-Zalesskii property |
| topic | Group Theory 20E26, 20E18 |
| url | https://arxiv.org/abs/2208.04058 |