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Article overview
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Explicit Helfgott type growth in free products and in limit groups | J. O. Button
; | Date: |
1 Sep 2011 | 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. | Source: | arXiv, 1109.0244 | Services: | Forum | Review | PDF | Favorites |
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