Profinite properties of residually free groups
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910680883396608 |
|---|---|
| author | Morales, Ismael |
| author_facet | Morales, Ismael |
| contents | Henry Wilton classified when a prime three-manifold $M$ has a residually free fundamental group $π_1 M$. We prove that the groups $π_1 M\times \mathbb Z^n$ are profinitely rigid within finitely generated residually free groups. We also establish other profinite invariants of the class of residually free groups such as coherence and subgroup separability. In the course of our proofs, we generalise a lemma of Wilton and Zalesskii on profinitely recognising when a central extension of groups splits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_13082 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Profinite properties of residually free groups Morales, Ismael Group Theory 20E18, 20E26 Henry Wilton classified when a prime three-manifold $M$ has a residually free fundamental group $π_1 M$. We prove that the groups $π_1 M\times \mathbb Z^n$ are profinitely rigid within finitely generated residually free groups. We also establish other profinite invariants of the class of residually free groups such as coherence and subgroup separability. In the course of our proofs, we generalise a lemma of Wilton and Zalesskii on profinitely recognising when a central extension of groups splits. |
| title | Profinite properties of residually free groups |
| topic | Group Theory 20E18, 20E26 |
| url | https://arxiv.org/abs/2306.13082 |