Powers of sets in free groups
Group Theory
2015-05-18 v2
Abstract
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.
Cite
@article{arxiv.1005.1820,
title = {Powers of sets in free groups},
author = {Stanislav Safin},
journal= {arXiv preprint arXiv:1005.1820},
year = {2015}
}
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3 pages