Radio nuclei in elliptical galaxies.

Observations at 4.9 GHz with the VLA are presented for 36 radio galaxies of the B2 and 3C catalogue, with no previous core flux measurement; 24 cores were detected, while for the others stringent upper limits are given. The statistical properties of the radio cores in elliptical galaxies are then analyzed, using a sample of 187 radio galaxies, which cover a power range from 10^23^ to 10^28^ W Hz^-1^. Correlations are found between the core power and the total power and between the core power and the optical absolute magnitude, in agreement with previous results; no redshift dependence is found of the two correlations. The existence of radio galaxies with upper limits to the core flux well below the value expected from the P_c_-P_t_ correlation suggests that these could be relic radio sources, where the nucleus has ceased its activity.