This proposal aims to facilitate close collaboration between researchers in the UK, Italy, USA and India to study the nature and consequences of the energy transferred from supermassive black holes at the centres of galaxies to the surrounding intergalactic medium (IGM) in groups of galaxies. The research combines data from opposite ends of the electromagnetic spectrum: low-frequency radio observations track the history of outbursts from the black holes, while X-ray data allow us to determine their effects on the ten-million-Kelvin gas of the IGM. The partner institutions have long records of internationally-recognised research in these areas. The University of Birmingham is one of the top few teams worldwide in the study of groups with a solid track record in X-ray astronomy (particularly using ESA's XMM-Newton X-ray observatory), while the INAF-Istituto di Radioastronomia provide access to some of Europe's best experts in the low-frequency radio regime. The Smithsonian Astrophysical Observatory (US) is the home of NASA's Chandra X-ray observatory, and has a strong claim as the preeminent X-ray astronomy institution worldwide, while the National Centre for Radio Astrophysics (India) operates the Giant Meterwave Radio Telescope (GMRT), the first and currently the only radio observatory to achieve high spatial resolution and sensitivity at low frequencies. The collaboration will bring together experts with diverse skills to study closely one of the outstanding puzzles of modern astrophysics, providing direct benefits to the European institutions involved, the wider scientific community, and to the European Research Area as a whole, through increased scientific returns from current European facilities, increased access to international resources, and the scientific and theoretical tools for wide range of future studies with Europe-based facilities (e.g., the European LOFAR radio observatory and ESA International X-ray Observatory).