Free factors and profinite completions
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866909296081502208 |
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| author | Garrido, Alejandra Jaikin-Zapirain, Andrei |
| author_facet | Garrido, Alejandra Jaikin-Zapirain, Andrei |
| contents | Can one detect free products of groups via their profinite completions? We answer positively among virtually free groups. More precisely, we prove that a subgroup of a finitely generated virtually free group $G$ is a free factor if and only if its closure in the profinite completion of $G$ is a profinite free factor. This generalises results by Parzanchevski and Puder (later also proved by Wilton) for free groups. Our methods are entirely different to theirs, combining homological properties of profinite groups and the decomposition theory of Dicks and Dunwoody. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_00912 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Free factors and profinite completions Garrido, Alejandra Jaikin-Zapirain, Andrei Group Theory 20E18, 20E06 Can one detect free products of groups via their profinite completions? We answer positively among virtually free groups. More precisely, we prove that a subgroup of a finitely generated virtually free group $G$ is a free factor if and only if its closure in the profinite completion of $G$ is a profinite free factor. This generalises results by Parzanchevski and Puder (later also proved by Wilton) for free groups. Our methods are entirely different to theirs, combining homological properties of profinite groups and the decomposition theory of Dicks and Dunwoody. |
| title | Free factors and profinite completions |
| topic | Group Theory 20E18, 20E06 |
| url | https://arxiv.org/abs/2207.00912 |