# On the profinite rigidity of free and surface groups

@inproceedings{Morales2022OnTP, title={On the profinite rigidity of free and surface groups}, author={Ismael Morales}, year={2022} }

. Let S be a free or surface group. We establish a Tits alternative for groups in the ﬁnite, soluble and p -genus of S . This generalises (and gives a new proof of) the analogous result of Baumslag for parafree groups. Then we study applications to proﬁnite rigidity. A well-known question of Remeslennikov asks whether a ﬁnitely generated residually ﬁnite G with proﬁnite completion b G ∼ = b S is necessarily G ∼ = S . We give a positive answer when G belongs to a class of groups H ab that has a…

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