Observations of early-type dwarf galaxies in clusters often show that cluster dwarf members have significantly higher velocities and less symmetric distributions than cluster giant ellipticals, suggesting that these dwarfs are recently accreted galaxies, possibly from an infalling group. We use a series of $N$-body simulations, exploring a parameter space of groups falling into clusters, to study the observed velocity distributions of the infall components along various lines of sight. We show that, as viewed along a line of sight parallel to the groups infall direction, there is a significant peculiar velocity boost during the pericentric passage of the group, and an increase in velocity dispersion that persists for many Gyr after the merger. The remnants of the infalling group, however, do not form a spatially distinct system -- consistent with recent observations of dwarf galaxies in the Virgo and Fornax clusters. This velocity signature is completely absent when viewed along a direction perpendicular to the merger. Additionally, the phase-space distribution of radial velocity along the infall direction versus cluster-centric radius reveals the separate dynamical evolution of the groups central core and outer halo, including the presence of infalling remnants outside the escape velocity envelope of the system. The distinct signature in velocity space of an infalling groups galaxies can therefore prove important in understanding the dynamical history of clusters and their dwarfs. Our results suggest that dwarf galaxies, being insensitive to dynamical friction, are excellent probes of their host clusters dynamical histories.
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