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Mar 8, 2022 at 20:49 comment added YCor @M.Winter yes this is precisely Grigorchuk's argument.
Mar 8, 2022 at 16:48 comment added M. Winter This follows also e.g. from the existence of Cayley graphs with a wide range of growth behaviors, which is a quasi-isometric invariant.
Mar 8, 2022 at 16:38 vote accept Dominic van der Zypen
Mar 8, 2022 at 14:03 comment added YCor I think this result is originally due to Grigorchuk (maybe be with 4 rather than 2 generators).
Mar 8, 2022 at 13:53 history answered George K CC BY-SA 4.0