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| Home > Articles > Published articles > A Note on the continuous extensions of injective morphisms between free groups to relatively free profinite groups |
| Date: | 2003 |
| Abstract: | 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. |
| Rights: | Tots els drets reservats.  |
| Language: | Anglès |
| Document: | Article ; recerca ; Versió publicada |
| Subject: | Profinite topology ; Rank of subgroups of free groups ; Monomorphisms between free groups |
| Published in: | Publicacions matemàtiques, V. 47 N. 2 (2003) , p. 477-487, ISSN 2014-4350 |
