We present new Giant Metrewave Radio Telescope observations at 235 MHz and 610 MHz of 18 X-ray bright galaxy groups. These observations are part of an extended project, presented here and in future papers, which combines low-frequency radio and X-ray data to investigate the interaction between central active galactic nuclei (AGN) and the intra-group medium (IGM). The radio images show a very diverse population of group-central radio sources, varying widely in size, power, morphology and spectral index. Comparison of the radio images with Chandra and XMM-Newton X-ray images shows that groups with significant substructure in the X-ray band and marginal radio emission at >= 1 GHz host low-frequency radio structures that correlate with substructures in IGM. Radio-filled X-ray cavities, the most evident form of AGN/IGM interaction in our sample, are found in half of the systems, and are typically associated with small, low- or mid-power double radio sources. Two systems, NGC5044 and NGC4636, possess multiple cavities, which are isotropically distributed around the group center, possibly due to group weather. In other systems the radio/X-ray correlations are less evident. However, the AGN/IGM interaction can manifest itself through the effects of the high-pressure medium on the morphology, spectral properties and evolution of the radio-emitting plasma. In particular, the IGM can confine fading radio lobes in old/dying radio galaxies and prevent them from dissipating quickly. Evidence for radio emission produced by former outbursts that coexist with current activity is found in six groups of the sample.
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