Powers of sets in free groups

Details Powers of sets in free groups Powers of sets in free groups

2010-05-11

arxiv.org/abs/1005.1820v1

Mathematics

Group Theory

3 pages

Scientific paper

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.

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