  Let $\cL$ be a homogeneous left invariant differential operator on a Carnot
group. Assume that both $\cL$ and $\cL^t$ are hypoelliptic. We study the
removable sets for $\cL$-solutions. We give precise conditions in terms of the
Carnot--Carath\'eodory Hausdorff dimension for the removability for
$\cL$-solutions under several auxiliary integrability or regularity hypotheses.
In some cases, our criteria are sharp on the level of the relevant Hausdorff
measure. One of the main ingredients in our proof is the use of novel local
self similar tilings in Carnot groups.
