Timeline for SQ-universality in the class of amenable groups
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
|
|
| Sep 25, 2011 at 2:56 | vote | accept | Denis Osin | ||
| Sep 25, 2011 at 1:35 | answer | added | Simon Thomas | timeline score: 10 | |
| Sep 24, 2011 at 23:22 | answer | added | user6976 | timeline score: 5 | |
| Sep 24, 2011 at 22:21 | comment | added | Denis Osin | In fact, the Folner function of every solvable group is bounded by an iterated exponential function, where the number of iterations is at most the solvability degree. It follows from the estimates in the paper of Erschler and the fact that every group of type $F/[R,R]$ embeds into the wreath product of $Z^n$ and $F/R$. In particular, all solvable groups have Fol bounded by some universal function. So there is no hope to prove Conjecture 1 just by using solvable groups. Interestingly, the solution announced by Anna uses locally finite-by-cyclic groups, which are elementary amenable | |
| Sep 24, 2011 at 22:16 | history | edited | Denis Osin | CC BY-SA 3.0 |
added 12 characters in body
|
| Sep 24, 2011 at 21:47 | comment | added | Denis Osin | This is a nice observation, but unfortunately it does not help. The groups considered there are free solvable groups of increasing solvability degree. There are only countably many of them. Hence their restricted direct product (and therefore every such a group) embeds in a 2-generated amenable group. | |
| Sep 24, 2011 at 21:15 | comment | added | Valerio Capraro | An observation that might be stupid, but maybe is related to your queston: in G.N. Arzhantseva, V.S. Guba, L.Guyot, Growth rates of amenable groups, Journal of Group Theory, 8 (2005), no.3, 389-394 the authors proved that a f.g. amenable group can have balls that increase very rapidly. I am not sure it makes sense but maybe this behavior of the balls can be reflected in the fact that Folner's condition is verified for very large sets. | |
| Sep 24, 2011 at 20:52 | history | edited | Denis Osin | CC BY-SA 3.0 |
deleted 1 characters in body; edited body
|
| Sep 24, 2011 at 20:44 | history | asked | Denis Osin | CC BY-SA 3.0 |