A note on the continuous extensions of injective morphisms between free groups to relatively free profinite groups
نویسندگان
چکیده
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 φ̂ 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 φ̂ can be asserted, or at least decided, and we draw a few corollaries. 2000 MSC 20E18, 20E05
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