It is definitely possible to install hardwood flooring over a concrete slab.
The one thing an installer has to look out for when installing over a concrete slab is the moisture of the concrete, which can cause the flooring to expand or contract. To avoid warping, the installer should preform extensive moisture tests on the sub floor and the hardwood flooring.
The method of installing over concrete that we highly recommend is using a vapor retarder and plywood as a moisture barrier. This eliminates most of the risk involved with moisture, and provides a sub floor for the nails.
It is important to tape all seams of the plastic and then float the plywood on top at a 45 degree angle. This helps prevent cracks along the seams of the panels of plywood.
Another method we have used with good results is gluing the hardwood flooring directly to the concrete slab. It is important to use the correct type of glue, like PL Premium. This method should only be done by an experience installer who understands how to manage moisture of concrete.