  We present the first results of our study of a sample of 101 X-ray galaxy
groups and clusters, which is volume-limited in each of three X-ray luminosity
bins. The aim of this work is to study the properties of the innermost ICM in
the cores of our groups and clusters, and to determine the effect of
non-gravitational processes, such as active galactic nucleus (AGN) feedback, on
the ICM. The entropy of the ICM is of special interest, as it bears the imprint
of the thermal history of a cluster, and it also determines a cluster's global
properties. Entropy profiles can therefore be used to examine any deviations
from cluster self-similarity, as well as the effects of feedback on the ICM. We
find that the entropy profiles are well-fitted by a simple powerlaw model, of
the form $K(r) = \alpha\times(r/100 \rm{kpc})^{\beta}$, where $\alpha$ and
$\beta$ are constants. We do not find evidence for the existence of an "entropy
floor", i.e. our entropy profiles do not flatten out at small radii, as
suggested by some previous studies.
