  We present AGN feedback in the interesting cases of two groups: AWM 4 and NGC
5044. AWM 4 is characterized by a combination of properties which seems to defy
the paradigm for AGN heating in cluster cores: a flat inner temperature profile
indicative of a past, major heating episode which completely erased the cool
core, as testified by the high central cooling time (> 3 Gyrs) and by the high
central entropy level (~ 50 keV cm^2), and yet an active central radio galaxy
with extended radio lobes out to 100 kpc, revealing recent feeding of the
central massive black hole. A recent Chandra observation has revealed the
presence of a compact cool corona associated with the BCG, solving the puzzle
of the apparent lack of low entropy gas surrounding a bright radio source, but
opening the question of its origin. NGC 5044 shows in the inner 10 kpc a pair
of cavities together with a set of bright filaments. The cavities are
consistent with a recent AGN outburst as also indicated by the extent of dust
and H_alpha emission even though the absence of extended 1.4 GHz emission
remains to be explained. The soft X-ray filaments coincident with H_alpha and
dust emission are cooler than those which do not correlate with optical and
infrared emission, suggesting that dust-aided cooling can contribute to the
overall cooling. For the first time sloshing cold fronts at the scale of a
galaxy group have been observed in this object.
