# Freiman's theorem in an arbitrary abelian group

```@article{Green2005FreimansTI,
title={Freiman's theorem in an arbitrary abelian group},
author={Ben Green and Imre Z. Ruzsa},
journal={Journal of the London Mathematical Society},
year={2005},
volume={75}
}```
• Published 10 May 2005
• Mathematics
• Journal of the London Mathematical Society
A famous result of Freiman describes the structure of finite sets A ⊆ ℤ 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.
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