Timeline for Finitely presented non-residually amenable groups without free subgroups
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| May 2, 2020 at 17:26 | answer | added | YCor | timeline score: 4 | |
| May 2, 2020 at 16:50 | history | edited | Isaac | CC BY-SA 4.0 |
edited title
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| May 2, 2020 at 13:35 | history | edited | Isaac | CC BY-SA 4.0 |
added 3 characters in body
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| May 1, 2020 at 22:41 | comment | added | YCor | Yes it has no free subgroup (as the whole group of continuous piecewise homographies of $P^1$ fixing $\infty$) — sorry I thought I wrote it | |
| May 1, 2020 at 22:37 | comment | added | Isaac | Let us continue this discussion in chat. | |
| May 1, 2020 at 22:24 | comment | added | Isaac | And how do you know it doesn’t contain a free group? | |
| May 1, 2020 at 22:22 | comment | added | YCor | Then the group of piecewise homographies constructed by Monod and Lodha-Moore should work. Indeed I think each such group $G$ (which is finitely presented and non-amenable) has all its proper quotients metabelian (and $G''$ is simple), so it's not residually amenable. It's locally indicable, has no infinite Property T subgroup. | |
| May 1, 2020 at 22:03 | comment | added | Isaac | What I really want is a finitely presented group that is not residually amenable and contains no free subgroup. Of course if the group has property T and is not residually finite then it is also not residually amenable. | |
| May 1, 2020 at 21:55 | comment | added | Isaac | I want it not to be residually finite. | |
| May 1, 2020 at 21:07 | history | asked | Isaac | CC BY-SA 4.0 |