Profinite Completions and Continuous Extensions of Morphisms Between Free Groups and Theirs Profinite Completions
DOI:
https://doi.org/10.5644/SJM.05.2.01Keywords:
Pseudovariety, free group, profinite topology, profinite group, profinite completionAbstract
It is known that every morphism $\varphi : F \rightarrow F'$ between free groups of pseudovariety $ \mathbf{V}$ of finite groups is uniformly continuous when both groups are equipped with their respective pro-$ \mathbf{V}$ topologies. In this paper we prove that this morphism can be uniquely extended to a continuous morphism between their pro-$ \mathbf{V}$ completions $\hat{\varphi} : \hat{F} \rightarrow \hat{F'}$?
2000 Mathematics Subject Classification. 20E18; 20E05
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