English

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.

Keywords

Cite

@article{arxiv.1005.1820,
  title  = {Powers of sets in free groups},
  author = {Stanislav Safin},
  journal= {arXiv preprint arXiv:1005.1820},
  year   = {2015}
}

Comments

3 pages

R2 v1 2026-06-21T15:21:11.259Z