APPROXIMATE GROUPS, II: THE SOLVABLE LINEAR CASE

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.