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We present a statistical study of several fundamental properties of radiosources in nearby clusters, including the radial distribution within clusters,the radio luminosity function (RLF), and the fraction of galaxies that isradio-active (radio active fraction, RAF). The analysis is carried out for asample of 573 clusters detected in the X-ray and also observed at 1.4 GHz inthe NVSS. K-band data from the 2MASS are used to identify the brightest clustergalaxies (BCGs), and to construct the K-band LF. Our main results include: (1)The surface density profile of radio-loud AGNs is much more concentrated thanthat of all galaxies, and can be described by the NFW profile withconcentration ~ 25. (2) A comparison of the RLFs in the clusters and in thefield shows that the cluster AGN number density is about 5,700 times higher,corresponding to a factor of 6.8 higher probability of a galaxy being radioactive in the cluster than in the field. We suggest that about 40-50% ofradio-loud AGNs in clusters may reside in low mass galaxies (M_K>-23). (3) TheRAFs of cluster galaxies of different stellar mass are estimated. About 5% ofgalaxies more luminous than the characteristic luminosity (M_K<M_*~-24) hostradio-loud AGNs. The RAF for BCGs is >30%, and depends on the cluster mass.Compare to the field population, cluster galaxies have 5-10 times higher RAF.Combining the AGN RLF and spatial distribution within clusters, we estimatethat they may inject an energy of ~0.13 keV per particle to the intraclustermedium near the cluster center. We also investigate the degree of contaminationby cluster radio sources on the yields of SZE cluster surveys, and estimatethat as many as 10% of clusters detected at 150 GHz may host AGNs whose flux iscomparable to the cluster SZE signal. (abridged)Comment: ApJS, in press; 27 pages, 16 figure

Radio Sources in Galaxy Clusters: Radial Distribution, and 1.4 GHz andK‐band Bivariate Luminosity Function