Explicit Helfgott type growth in free products and in limit groups
| Autor: | Button, J. O. |
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| Rok vydání: | 2011 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Minor reordering; ends with some questions |
| Databáze: | arXiv |
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