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We present a statistical survey of the properties of 148 radio sources that are highly likely to be in AbeI1 clusters, and compare them with 127 identified field sources with the same range of redshifts from the Culgoora-3 list.We show that: (i) the sources are highly concentrated towards the cluster centres; (ii) the probability of finding a source in a cluster is independent of cluster richness; (iii) the sources occur relatively much more frequently in Bautz-Morgan (B-M) I clusters; (iv) the spectral index is not dependent on cluster richness but increases towards the cluster centres and is highest in clusters of morphological class B-M I; (v) the radio power P160 is highest for sources within 0·10 AbeIl radius of cluster centres but does not depend on a cluster's richness or its optical morphology; the linear sizes of radio galaxies do not depend upon cluster richness, distance from the cluster centre or optical morphology.A comparison of the properties of sources in clusters with those of the Culgoora-3 field sample shows: (i) the spectral indices of cluster sources are higher than spectral indices of field sources, particularly if the cluster sources are near cluster centres and/or in B-M I clusters; (ii) there is significant second-degree and third-degree curvature in the spectra of both cluster and field sources but the curvature is more pronounced in the cluster sample; (iii) the sources in clusters are not particularly powerful, i.e. field sources emit a median P160 which is ~ 4 times that of cluster sources; (iv) the cluster sources have a median overall linear dimension that is ~ 130 kpc smaller than that of the field sources, a decrease which is not due to the lower power of cluster sources; (v) the luminosity functions for both cluster and field sources have a power-law form and possess very similar power-law exponents, only about 20 % of radio galaxies with 0·02 < z < 0·20 being located in rich clusters.Our results support the hypothesis that the spectra and dimensions of radio sources in clusters are influenced by a hot, relatively dense electron gas and that radio observations are more sensitive detectors of this gas than are existing optical or X-ray studies.

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