= The structure of approximate groups by Emmanuel Breuillard and others
{c}
{tag=Work by Emmanuel Breuillard}
{tag=Work by Ben Green}
{tag=Work by Terence Tao}
{title2=2012}
Published article: https://pmihes.centre-mersenne.org/articles/10.1007/s10240-012-0043-9/
Author-hosted full text: https://www.imo.universite-paris-saclay.fr/~emmanuel.breuillard/structure.pdf
Theorem 2.10 gives the approximate-group structure theorem. Corollary 11.9 and its proof, pages 68–69 in the inspected author version, obtain a bounded-index finite-by-nilpotent structure from one-scale relative polynomial growth. The proof uses a smaller scale with bounded growth; fixed scale constants may be adjusted by increasing the threshold.
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