Freiman's theorem in an arbitrary abelian group
Copyright policy )Freiman's theorem in an arbitrary abelian group
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.
15 pages, to appear in London Math. Society journals. Exceptionally minor cosmetic changes from the previous version
- University of Bristol United Kingdom
- International Centre for Mathematical Sciences United Kingdom
- University of Oxford United Kingdom
- Hungarian Academy of Sciences Hungary
Mathematics - Number Theory, Inverse problems of additive number theory, including sumsets, Sequences and sets, inverse problem of additive number theory, multidimensional arithmetic progressions, 510, 004, Other combinatorial number theory, Freiman's theorem, FOS: Mathematics, coset progressions, Mathematics - Combinatorics, Number Theory (math.NT), Combinatorics (math.CO), Abelian groups
Mathematics - Number Theory, Inverse problems of additive number theory, including sumsets, Sequences and sets, inverse problem of additive number theory, multidimensional arithmetic progressions, 510, 004, Other combinatorial number theory, Freiman's theorem, FOS: Mathematics, coset progressions, Mathematics - Combinatorics, Number Theory (math.NT), Combinatorics (math.CO), Abelian groups
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