A Note on the continuous extensions of injective morphisms between free groups to relatively free profinite groups
Let V be a pseudovariety of finite groups such that free groups are residually V, and let ϕ: F(A) → F(B) be an injective morphism between finitely generated free groups. We characterize the situations where the continuous extension ˆϕ of ϕ between the pro-V completions of F(A) and F(B) is also injec...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2003 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:2019 |
| Acceso en línea: | https://ddd.uab.cat/record/2019 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_47203_10 |
| Access Level: | acceso abierto |
| Palabra clave: | Profinite topology Rank of subgroups of free groups Monomorphisms between free groups |
| Sumario: | Let V be a pseudovariety of finite groups such that free groups are residually V, and let ϕ: F(A) → F(B) be an injective morphism between finitely generated free groups. We characterize the situations where the continuous extension ˆϕ of ϕ between the pro-V completions of F(A) and F(B) is also injective. In particular, if V is extension-closed, this is the case if and only if ϕ(F(A)) and its pro-V closure in F(B) have the same rank. We examine a number of situations where the injectivity of ˆϕ can be asserted, or at least decided, and we draw a few corollaries. |
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