# Amenability and profinite completions of finitely generated groups

@inproceedings{Kionke2021AmenabilityAP, title={Amenability and profinite completions of finitely generated groups}, author={Steffen Kionke and E. Schesler}, year={2021} }

This article explores the interplay between the finite quotients of finitely generated residually finite groups and the concept of amenability. We construct a finitely generated, residually finite, amenable group A and an uncountable family of finitely generated, residually finite non-amenable groups all of which are profinitely isomorphic to A. All of these groups are branch groups. Moreover, picking up Grothendieck’s problem, the group A embeds in these groups such that the inclusion induces… Expand

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