Free factors and profinite completions
| Autor: | Garrido, Alejandra, Jaikin-Zapirain, Andrei |
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| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | International Mathematics Research Notices, Volume 2023, Issue 24, December 2023, Pages 21320--21345 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1093/imrn/rnac309 |
| Popis: | 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. Comment: 21 pages, accepted for publication in IMRN |
| Databáze: | arXiv |
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