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In an unpublished note, Green proved that such a result does not necessarily hold in nonabelian groups if s ≥ 64.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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Research is partially supported by OTKA grants K 67676, K 81658 and Balaton Program Project.
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Hegyvári, N., Hennecart, F. A note on Freiman models in Heisenberg groups. Isr. J. Math. 189, 397–411 (2012). https://doi.org/10.1007/s11856-011-0175-5
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DOI: https://doi.org/10.1007/s11856-011-0175-5