Timeline for Existence of any strong form of Folner condition for elementary amenable groups
Current License: CC BY-SA 3.0
9 events
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| Jan 8, 2017 at 11:56 | comment | added | YCor | The last question seems to be whether there exists $f$ such that if the Følner function of $G$ is $O(f)$ then $G$ is virtually solvable. There exists non-virtually-solvable $G$ with exponential Følner function (wreath product $F\wr\mathbf{Z}$ with $F$ finite non-solvable). If $f$ is smaller, the only $G$ with Følner function $O(f)$ have subexponential growth (and hence the virtually solvable ones will have polynomial growth). So I'm not sure this is of much interest since it will miss most virtually solvable groups. | |
| Jan 8, 2017 at 8:26 | comment | added | Alireza Abdollahi | @YCor Another way, if we assume that the size of the Folner set (which is depending to $A$ and $\epsilon$) is bounded above by a function $f:\mathbb{R}^+\rightarrow \mathbb{R}^+$ of $\epsilon$ only. Under what conditions on $f$ one can conclude that the group is virtually solvable. | |
| Jan 8, 2017 at 8:25 | history | edited | Alireza Abdollahi | CC BY-SA 3.0 |
added 279 characters in body
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| S Jan 8, 2017 at 8:18 | history | suggested | Martin Sleziak |
added (amenability) tag
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| Jan 8, 2017 at 7:46 | review | Suggested edits | |||
| S Jan 8, 2017 at 8:18 | |||||
| S Jan 8, 2017 at 3:32 | history | suggested | CommunityBot | CC BY-SA 3.0 |
Typo in title.
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| Jan 8, 2017 at 3:11 | review | Suggested edits | |||
| S Jan 8, 2017 at 3:32 | |||||
| Jan 7, 2017 at 13:59 | comment | added | YCor | "Elementary amenable" is a very poor choice of terminology (due to Day?): it doesn't mean more amenable than other amenable, it means constructible in some way that makes its amenability obvious. There are many quantitative ways to measure amenability (Følner function, for instance). I'm not sure there is any universal bound for Følner functions of elementary amenable groups. (Another bad thing about this terminology is that it makes it somewhat rely on amenability -at least in people's mind-, while amenability is of analytical nature and not elementary amenable.) | |
| Jan 7, 2017 at 12:24 | history | asked | Alireza Abdollahi | CC BY-SA 3.0 |