Dan Sălăjan
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 May 8 awarded Yearling Sep 13 awarded Necromancer Jul 2 awarded Curious May 8 awarded Yearling Dec 11 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 9 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 Sep 4 awarded Enthusiast