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 φ : F → F'? 2000 Mathematics Subject Classification. 20E18; 20E05