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Jun 19, 2022 at 7:45 comment added YCor Just as a comment, exponential growth of standard wreath products (namely of $A\wr B$ for $A\neq 1$ and $B$ infinite f.g.) is folklore and well-known, and it was quite a surprise when Bartholdi and Erschler came up in 2011 with (permutational) wreath products of subexponential growth.
Jun 19, 2022 at 7:24 answer added Ville Salo timeline score: 2
Jun 17, 2022 at 20:27 comment added Ville Salo Isn't the answer to the first question trivially "yes"? The answer to the second is "no": for any $G$ which is is countably infinite, finitely generated, amenable and torsion, the group $\mathbb{Z}_2 \wr G$ has exponential growth.
Jun 17, 2022 at 19:46 history edited LSpice CC BY-SA 4.0
Folner -> Følner
Jun 17, 2022 at 19:44 history edited YCor CC BY-SA 4.0
fixed typo
S Jun 17, 2022 at 19:35 review First questions
Jun 17, 2022 at 19:51
S Jun 17, 2022 at 19:35 history asked Jacob R CC BY-SA 4.0