We report evidence that the gas properties of X- ray groups containing radio galaxies differ from those of radio- quiet groups. For a well- studied sample of ROSAT- observed groups, we found that more than half of the elliptical- dominated groups can be considered 'radio- loud', and that radio- loud groups are likely to be hotter at a given X- ray luminosity than radio- quiet groups. We tested three different models for the origin of the effect and conclude that radio- source heating is the most likely explanation. We found several examples of groups where there is strong evidence from Chandra or XMM- Newton images for interactions between the radio source and the group gas. A variety of radio- source heating processes are important, including shock- heating by young sources and gentler heating by larger sources. The heating effects can be longer- lasting than the radio emission. We show that the sample of X- ray groups used in our study is not significantly biased in the fraction of radio- loud groups that it contains. This allows us to conclude that the energy per particle that low- power radio galaxies can inject over the group lifetime is comparable to the requirements of structure formation models.