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

ABSTRACT Green and Ruzsa recently proved that for any s ≥ 2, any small squaring set A in a (multiplicative) abelian group, i.e., |A·A| < K|A|, has a Freiman smodel: it means that there exists a group G and a Freiman s-isomorphism from A into G such that |G| < f (s,K)|A|.

In an unpublished note, Green proved that such a result does not necessarily hold in nonabelian groups if s ≥ 64. The aim of this paper is improve Green’s result by showing that it remains true under the weaker assumption s ≥ 6.

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