We present gas temperature, density, entropy and cooling time profiles for the cores of a sample of 15 galaxy groups observed with Chandra.We find that the entropy profiles follow a power-law profile down to very small fractions of R500. Differences between the gas profiles of groups with radio loud and radio quiet BGGs are only marginally significant, and there is only a small difference in the LX : TX relations, for the central regions we study with Chandra, between the radio-loud and radio-quiet objects in our sample, in contrast to the much larger difference found on scales of the whole group in earlier work. However, there is evidence, from splitting the sample based on the mass of the central black holes, that repeated outbursts of AGN activity may have a long term cumulative effect on the entropy profiles. We argue that, to first-order, energy injection from radio sources does not change the global structure of the gas in the cores of groups, although it can displace gas on a local level. In most systems, it appears that AGN energy injection serves primarily to counter the effects of radiative cooling, rather than being responsible for the similarity breaking between groups and clusters.