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arXiv:math/0505198 [math.NT]AbstractReferencesReviewsResources

Freiman's Theorem in an arbitrary abelian group

Ben Green, Imre Z. Ruzsa

Published 2005-05-10, updated 2006-02-07Version 2

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.

Comments: 15 pages, to appear in London Math. Society journals. Exceptionally minor cosmetic changes from the previous version
Categories: math.NT, math.CO
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