Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am reading an introduction to growth of groups. The notions of polynomial and superpolynomial growth are introduced, as are exponential and subexponential growth.

I can prove that the growth of a group is always either exponential or subexponential (it is exercise 1.6). However, there seems to be no mention of an analogous result for (super)polynomial growth (i.e. the growth of a group is always either polynomial or superpolynomial).

There exist strictly increasing functions which grow faster than polynomially but are not superpolynomial (this is pretty clear; a more detailed explanation can be found in the second section of this document), but I do not know whether these occur as the growth function of some group.

The thesis of a Nick Scott claims to prove that every group grows either polynomially or superpolynomially, but I don't see it (it is in subsection 1.4.1, on p.12; it seems to me the proof assumes that the limit $\log(\beta(k))/\log(k)$ exists, but I don't know why).

So my question is: does every group grow either polynomially or superpolynomially?

share|improve this question
    
I would suggest posting this question on Math Overflow. –  Jim Belk Apr 25 '12 at 21:43
1  
I posted the question on Math Overflow. –  Daan Michiels Apr 25 '12 at 22:19

1 Answer 1

up vote 1 down vote accepted

The question has been answered on Math Overflow. The answer is yes, by the way.

share|improve this answer
1  
You might as well accept your answer as well to show that this question has now been dealt with. –  Tara B Apr 26 '12 at 9:21
    
Yes, I tried this. It says "you can accept your own answer tomorrow". –  Daan Michiels Apr 26 '12 at 13:39

Your Answer

 
discard

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

Not the answer you're looking for? Browse other questions tagged or ask your own question.