  The weak regular coherence is a coarse property of a finitely generated group
$\Gamma$. It was introduced by G. Carlsson and this author to play the role of
a weakening of Waldhausen's regular coherence as part of computation of the
integral K-theoretic assembly map. A new class of metric spaces (sFDC) was
introduced recently by A. Dranishnikov and M. Zarichnyi. This class includes
most notably the spaces with finite decomposition complexity (FDC) studied by
E. Guentner, D. Ramras, R. Tessera, and G. Yu. The main theorem of this paper
shows that a group that has finite $K(\Gamma,1)$ and sFDC is weakly regular
coherent. As a consequence, the integral K-theoretic assembly maps are
isomorphisms in all dimensions for any group that has finite $K(\Gamma,1)$ and
FDC. In particular, the Whitehead group $Wh (\Gamma)$ is trivial for such
groups.
