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A Note on the continuous extensions of injective morphisms between free groups to relatively free profinite groups
Coulbois, Thierry
Sapir, Mark
Weil, Pascal

Data: 2003
Resum: 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.
Drets: Tots els drets reservats.
Llengua: Anglès.
Document: Article ; recerca ; article ; publishedVersion
Matèria: Profinite topology ; Rank of subgroups of free groups ; Monomorphisms between free groups
Publicat a: Publicacions matematiques, V. 47 N. 2 (2003) , p. 477-487, ISSN 0214-1493

DOI: 10.5565/PUBLMAT_47203_10

11 p, 136.6 KB

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