Freiman's theorem in an arbitrary abelian group

Ben Green, Imre Z. Ruzsa

Research output: Contribution to journalArticle

65 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)163-175
Number of pages13
JournalJournal of the London Mathematical Society
Issue number1
Publication statusPublished - Feb 2007

ASJC Scopus subject areas

  • Mathematics(all)

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