Abstract
We describe the structure of ‘K-approximate subgroups’ of solvable subgroups of GLn(ℂ), showing that they have a large nilpotent piece. By combining this with the main result of our recent paper on approximate subgroups of torsion-free nilpotent groups (E. Breuillard and B. J. Green, Approximate groups, I: the torsion-free nilpotent case, J. Inst. Math. Jussieu, to appear), we show that such approximate subgroups are efficiently controlled by nilpotent progressions.
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