We investigate the dynamical evolution of galaxies in groups with different formation epochs. Galaxy groups have been selected to be in different dynamical states, namely dynamically old and dynamically young, which reflect their early and late formation times, respectively, based on their halo mass assembly. The brightest galaxies in dynamically young groups have suffered their last major galaxy merger typically similar to 2 Gyr more recently than their counterparts in dynamically old groups. Furthermore, we study the evolution of velocity dispersion in these two classes and compare them with the analytic models of isolated halos. The velocity dispersion of dwarf galaxies in high-mass, dynamically young groups increases slowly in time, while the analogous dispersion in dynamically old, high-mass groups is constant. In contrast, the velocity dispersion of giant galaxies in low-mass groups decreases rapidly at late times. This increasing velocity bias is caused by dynamical friction, and starts much earlier in the dynamically old groups. The recent RADIO-SAGE model of galaxy formation suggests that radio luminosities of central galaxies, considered to be tracers of AGN activity, are enhanced in halos that assembled more recently, independent of the time since the last major merger.