A Product Theorem in Free Groups
نویسنده
چکیده
If A is a finite subset of a free group with at least two noncommuting elements then |A · A · A| ≥ |A| 2 (log |A|)O(1) . More generally, the same conclusion holds in an arbitrary virtually free group, unless A generates a virtually cyclic subgroup. The central part of the proof of this result is carried on by estimating the number of collisions in multiple products A1 · . . . · Ak. We include a few simple observations showing that in this “statistical” context the analogue of the fundamental Plünnecke-Ruzsa theory looks particularly simple and appealing.
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