  We construct a countable p-local group with a proper invariant metric whose
Assouad-Nagata dimension is strictly greater than the asymptotic dimension with
linear control. This solves Problem 8.6 from the list [Dr]. We study asymptotic
dimension with linear control $\ell$-$asdim_{\omega}$ that depends on a fixed
ultrafilter on the naturals. It turns out that the Assouad-Nagata dimension is
the supremum of $\ell$-$asdim_{\omega}$ on all $\omega$ and the asymptotic
dimension with linear control is the minimum.

Metric Geometry