Powers of sets in free groups

Stanislav Safin

Published 2010-05-11, updated 2012-11-23Version 2

We prove that |A^n| > c_n |A|^{[\frac{n+1}{2}]} for any finite subset A of a free group if A contains at least two noncommuting elements, where c_n>0 are constants not depending on A. Simple examples show that the order of these estimates are the best possible for each n>0.