  X-Ray observations of groups and clusters of galaxies show that the
Intra-Cluster Medium (ICM) in their cores is hotter than expected from
cosmological numerical simulations of cluster formation which include star
formation, radiative cooling and SN feedback. We investigate the effect of the
injection of supersonic AGN jets into the ICM using axisymmetric hydrodynamical
numerical simulations. A simple model for the ICM, describing the radial
properties of gas and the gravitational potential in cosmological N-Body+SPH
simulations of one cluster and three groups of galaxies at redshift z=0, is
obtained and used to set the environment in which the jets are injected. We
varied the kinetic power of the jet and the emission-weighted X-Ray temperature
of the ICM. The jets transfer their energy to the ICM mainly by the effects of
their terminal shocks. A high fraction of the injected energy can be deposited
through irreversible processes in the cluster gas, up to 75% in our
simulations. We show how one single, powerful jet can reconcile the predicted
X-Ray properties of small groups, e.g. the Lx-Tx relation, with observations.
We argue that the interaction between AGN jets and galaxy groups and cluster
atmospheres is a viable feedback mechanism.
