• Corpus ID: 253761506

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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