Freiman's Theorem in an arbitrary abelian group
Number Theory
2007-05-23 v2 Combinatorics
Abstract
A famous result of Freiman describes the structure of finite sets A of integers with small doubling property. If |A + A| <= K|A| then A is contained within a multidimensional arithmetic progression of dimension d(K) and size f(K)|A|. Here we prove an analogous statement valid for subsets of an arbitrary abelian group.
Cite
@article{arxiv.math/0505198,
title = {Freiman's Theorem in an arbitrary abelian group},
author = {Ben Green and Imre Z. Ruzsa},
journal= {arXiv preprint arXiv:math/0505198},
year = {2007}
}
Comments
15 pages, to appear in London Math. Society journals. Exceptionally minor cosmetic changes from the previous version