MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $G$ be an amenable group of exponential growth and let $S$ be a finite symmetric generating set. For each $k$, let $B_{k}$ be the closed ball of radius $k$ about the identity element in the corresponding Cayley graph of $G$ and let $b_{k} = |B_{k}|$. If $\lim b_{k+1}/b_{k}$ exists, then $\lim b_{k+1}/b_{k} = \lim b_{k}^{1/k} > 1$ and this easily implies that no subsequence of the $B_{k}$ forms a Folner sequence for $G$. But is this also true for those amenable groups of exponential growth for which $\lim b_{k+1}/b_{k}$ does not exist?

share|cite|improve this question
    
@Simon: I do not know any group for which the limit $\lim b_{k+1}/b_{k}$ does not exist. – Mark Sapir Oct 28 '10 at 15:21
    
@Mark: see mathoverflow.net/questions/36126/… – Andreas Thom Oct 28 '10 at 15:56

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.