科研之友
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摘要
If A is a finite subset of a free group with at least two noncommuting elements, then vertical bar A.A.A vertical bar >= vertical bar A vertical bar(2)/(log vertical bar A vertical bar)(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 A(1) . . . . A(k). We include a few simple observations showing that in this "statistical" context the analogue of the fundamental Pliinnecke-Ruzsa theory looks particularly simple and appealing.
- 出版日期2014-3
