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arXiv · 0912.0305

Approximate groups and doubling metrics

Tom Sanders
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Abstract

We develop a version of Freiman's theorem for a class of non-abelian groups, which includes finite nilpotent, supersolvable and solvable A-groups. To do this we have to replace the small doubling hypothesis with a stronger relative polynomial growth hypothesis akin to that in Gromov's theorem (although with an effective range), and the structures we find are balls in (left and right) translation invariant pseudo-metrics with certain well behaved growth estimates. Our work complements three other recent approaches to developing non-abelian versions of Freiman's theorem by Breuillard and Green, Fischer, Katz and Peng, and Tao.

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Tom Sanders. 2012-12-03. Approximate groups and doubling metrics. https://doi.org/10.1017/s0305004111000740

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