||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.
||Tots els drets reservats.
||Article ; recerca ; article ; publishedVersion
Profinite topology ;
Rank of subgroups of free groups ;
Monomorphisms between free groups
||Publicacions matematiques, V. 47 N. 2 (2003) , p. 477-487, ISSN 0214-1493