Article

# A note on Freiman models in Heisenberg groups

Israel Journal of Mathematics (Impact Factor: 0.65). 01/2010; 189(1):1-15. DOI: 10.1007/s11856-011-0175-5

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**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.06/2005; - [Show abstract] [Hide abstract]

**ABSTRACT:**We study a Szemer\'edi-Trotter type theorem in finite fields. We then use this theorem to obtain an improved sum-product estimate in finite fields.12/2007; -
**Sumsets and structure Combinatorial number theory and additive group theory**. . 87-210.

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