Geodesic
Powers of sets in free groups
Sbornik. Mathematics, Tome 202 (2011) no. 11, pp. 1661-1666

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove that $|A^n|\geqslant c_n\cdot|A|^{[(n+1)/2]}$ for any finite subset $A$ of a free group if $A$ contains at least two noncommuting elements, where the $c_n>0$ are constants not depending on $A$. Simple examples show that the order of these estimates is best possible for each $n>0$. Bibliography: 5 titles.
Keywords: free group, relations in a free group, subsets of a free group. 
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     author = {S. R. Safin},
     title = {Powers of sets in free groups},
     journal = {Sbornik. Mathematics},
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     number = {11},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2011_202_11_a4/}
}
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S. R. Safin. Powers of sets in free groups. Sbornik. Mathematics, Tome 202 (2011) no. 11, pp. 1661-1666. http://geodesic.mathdoc.fr/item/SM_2011_202_11_a4/