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- W2034865552 abstract "We adapt Safin's result on powers of sets in free groups to obtain Helfgott type growth in free products: if A is any finite subset of a free product of two arbitrary groups then either A is conjugate into one of the factors, or the size of the triple product AAA of A is at least 1/7776 times the square of |A|, or A generates an infinite cyclic or infinite dihedral group. We also point out that if A is any finite subset of a limit group then |AAA| satisfies the above inequality unless A generates a free abelian group. This gives rise to many infinite groups G where there exist c>0 and d=1 such that any finite subset A of G has the property that either |AAA| is at least c times (|A| to the power of 1+d) or it generates a virtually nilpotent group." @default.
- W2034865552 created "2016-06-24" @default.
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- W2034865552 date "2011-09-01" @default.
- W2034865552 modified "2023-09-24" @default.
- W2034865552 title "Explicit Helfgott type growth in free products and in limit groups" @default.
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- W2034865552 doi "https://doi.org/10.48550/arxiv.1109.0244" @default.
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