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Freiman's Theorem in an arbitrary abelian group

Research paper by Ben Green, Imre Z. Ruzsa

Indexed on: 06 Feb '06Published on: 06 Feb '06Published in: Mathematics - Number Theory



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.