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Sep
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awarded  Necromancer
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awarded  Curious
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awarded  Yearling
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comment An example of a non-amenable exact group without free subgroups.
I don't think the group above is known to be exact.
Nov
20
answered Uniform bounds on Kazhdan constants in groups
Nov
20
comment Uniform bounds on Kazhdan constants in groups
It seems so, by Gelander and Zuk ams.org/mathscinet/search/…
Nov
15
comment Folner sets and balls
Thanks so much for this beautiful post! Accidentally, I also analyzed this presentation (and I'm an old fan of the combinatorial hyperbolic plane). I need to think more about your intuition concerning arbitrarly generating sets.
Nov
15
comment Folner sets and balls
In general a free semigroup won't help you that much, since you need both lower and upper bounds estimation on the sizes of balls...
Nov
15
comment Folner sets and balls
It looks unlikely, nevertheless, I don't have a disproof. In fact, the shape of Folner sets in exponential growth groups is quite unclear to me, so I asked the most basic question I could come up with. I have no decent evidence for or against, but often enough the quantity $liminf c_{n+1}/c_n$, where $c_n$ is the size of the ball, is less than the growth... so it is not clear so far.
Nov
15
comment Folner sets and balls
Thanks for the comment. A sequence of balls in my phrasing was meant to be a subsequence of the sequence of the balls, indeed. I hope it is clear.
Nov
15
revised Folner sets and balls
edited body
Nov
15
asked Folner sets and balls
Nov
6
awarded  Nice Answer
Nov
4
answered Is there an infinite group with exactly two conjugacy classes?
Oct
19
answered New trends in Applied Graph Theory
Oct
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awarded  Caucus
Oct
9
answered Rotation numbers for amenable group actions on the circle
Oct
1
comment Speed of random walks in groups
You re welcome. Very interesting, I don´t know any reference or proof... I might think about it, maybe there is a simple reason for it. I let you know if I succeed. Dan
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4
awarded  Enthusiast
Aug
28
comment Expected edit distance
@Carl: No, that typo escaped 6 edits :).