  We have observed four X-ray underluminous groups of galaxies using the Giant
Meterwave RadioTelescope. The groups NGC 524, 720, 3607, and 4697 are
underluminous in relation to the extrapolation of the Lx - T relation from rich
clusters and do not show any evidence of current AGN activities that can
account for such a departure. The GMRT observations carried out at low
frequencies (235 and 610 MHz) were aimed at detecting low surface brightness,
steep-spectrum sources indicative of past AGN activities in these groups. No
such radio emissions were detected in any of these four groups. The
corresponding upper limits on the total energy in relativistic particles is
about 3 X 10$^{57}$ erg. This value is more than a factor of 100 less than that
required to account for the decreased X-ray luminosities (or, enhanced
entropies) of these four groups in the AGN-heating scenario. Alternatively, the
AGN activity must have ceased about 4 Gyr ago, allowing the relativistic
particles to diffuse out to such a large extent (about 250 kpc) that their
radio emission could have been undetected by the current observations. If the
latter scenario is correct, the ICM was pre-heated before the assembly of
galaxy clusters.
