Timeline for Is the infinite product of solvable groups amenable?
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 20, 2023 at 19:34 | vote | accept | Asgar | ||
| Aug 9, 2023 at 21:32 | comment | added | Carl-Fredrik Nyberg Brodda | @JimBelk Very nice! (And, for completeness, elementary arguments show that the depth-$n$ automorphism group is a $2$-group for all $n$). | |
| Aug 9, 2023 at 20:22 | comment | added | Jim Belk | @Carl-FredrikNybergBrodda For a very concrete example, there is a natural embedding of the automorphism group $\mathrm{Aut}(T_2)$ of an infinite rooted binary tree into the product of the autuomorphism groups of finite complete rooted binary trees of depth $n$, and nonabelian free subgroups of $\mathrm{Aut}(T_2)$ have been described explicitly as automata groups. | |
| Aug 7, 2023 at 19:37 | comment | added | Dave Benson | @Carl-FredrikNybergBrodda Yes, even better... | |
| Aug 7, 2023 at 19:34 | comment | added | Carl-Fredrik Nyberg Brodda | Indeed free groups are residually (finite $p$-groups), so there is an infinite product of finite nilpotent groups which is not amenable. | |
| Aug 7, 2023 at 19:11 | history | answered | Dave Benson | CC BY-SA 4.0 |