Abstract:
We prove that |An|⩾cn⋅|A|[(n+1)/2] for any finite subset A of a free group if A contains at least two noncommuting elements, where the cn>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.
\Bibitem{Saf11}
\by S.~R.~Safin
\paper Powers of sets in free groups
\jour Sb. Math.
\yr 2011
\vol 202
\issue 11
\pages 1661--1666
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This publication is cited in the following 11 articles:
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V. S. Atabekyan, V. G. Mikaelyan, “O proizvedenii podmnozhestv v pereodicheskikh gruppakh”, Proceedings of NAS RA. Mathematics, 2022, 12
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Emmanuel Breuillard, Ben Green, Terence Tao, Bolyai Society Mathematical Studies, 25, Erdős Centennial, 2013, 129
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