Profinite Completions and Continuous Extensions of Morphisms Between Free Groups and Theirs Profinite Completions - Lonza, Katija (Sarajevo Journal of Mathematics, 2024)
It is known that every morphism $φ : F → F'$ between free groups of pseudovariety $ V$ of finite groups is uniformly continuous when both groups are equipped with their respective pro-$ V$ topologies. In this paper we prove that this morphism can be uniquely extended to a continuous morphism between their pro-$ V$ completions $\hat{φ} : \hat{F} → \hat{F'}$? 2000 Mathematics Subject Classification. 20E18; 20E05