Profinite detection of free products and free factors
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
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| _version_ | 1866912971113889792 |
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| author | Jaikin-Zapirain, Andrei Souza, Henrique Zalesski, Pavel |
| author_facet | Jaikin-Zapirain, Andrei Souza, Henrique Zalesski, Pavel |
| contents | Let $G$ be the fundamental group of a graph of finitely generated virtually free groups with virtually cyclic edge groups. We shaw that $G$ is cohomologically good if $G$ is residually finite. If $G$ is LERF, we prove that G splits non-trivially as a free product if and only if its profinite completion $\widehat{G}$ splits non-trivially as a free profinite product. Moreover, we are able to detect one-ended free factors of $G$ from $\widehat{G}$. As an application, we deduce that any profinitely rigid word in a finitely generated free group is universally profinitely rigid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_16674 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Profinite detection of free products and free factors Jaikin-Zapirain, Andrei Souza, Henrique Zalesski, Pavel Group Theory Let $G$ be the fundamental group of a graph of finitely generated virtually free groups with virtually cyclic edge groups. We shaw that $G$ is cohomologically good if $G$ is residually finite. If $G$ is LERF, we prove that G splits non-trivially as a free product if and only if its profinite completion $\widehat{G}$ splits non-trivially as a free profinite product. Moreover, we are able to detect one-ended free factors of $G$ from $\widehat{G}$. As an application, we deduce that any profinitely rigid word in a finitely generated free group is universally profinitely rigid. |
| title | Profinite detection of free products and free factors |
| topic | Group Theory |
| url | https://arxiv.org/abs/2603.16674 |