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Sep 18, 2023 at 12:56 answer added mahdi meisami timeline score: 0
Jun 2, 2012 at 12:04 answer added Dima Savchuk timeline score: 6
Jun 1, 2012 at 19:10 comment added Igor Belegradek @Yves, thank you. @Ashot, I do not know the literature, which is why I ask here; there are of course other periodic amenable groups.
Jun 1, 2012 at 18:42 comment added Ashot Minasyan As far as I remember, Grigorchuk also constructs f.g. $p$-groups for $p \neq 2$ of intermediate growth. Could these serve as counterexamples?
Jun 1, 2012 at 17:14 comment added YCor certainly (1) does not help: indeed if your group is not locally finite, it contains an infinite f.g. subgroup and hence this subgroup also satisfies your requirements.
Jun 1, 2012 at 15:27 history edited Igor Belegradek CC BY-SA 3.0
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Jun 1, 2012 at 15:00 history asked Igor Belegradek CC BY-SA 3.0