Abstract
Recent claims in the literature for the existence of a low velocity dispersion population of galaxies in the cores of rich clusters are investigated. The suggested population, which has been generally interpreted as gravitationally bound to the potential well of the first-ranked cluster galaxy, is taken as evidence in support of the galactic cannibalism model for D/cD galaxy formation. Five clusters which have been suggested in the literature to possess bound population of galaxies associated with the D/cD are examined with a statistical test, which compares the number of galaxies with relative velocities less than a given fraction of the cluster scale to the number expected for an assumed parent velocity dispersion
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