Growth of the structure in the Universe manifest as accretion flows of galaxies onto groups and clusters. Thus, the present day properties of groups and their member galaxies are influenced by the characteristics of this continuous infall pattern. Several works both theoretical, in numerical simulations, and in observations, study this process and provide useful steps for a better understanding of galaxy systems and their evolution. We aim at exploring the streaming flow of galaxies onto groups using observational peculiar velocity data. The effects of distance uncertainties are also analyzed as well as the relation between the infall pattern and group and environment properties.This work deals with analysis of peculiar velocity data and their projection on the direction to group centers, to determine the mean galaxy infall flow. We applied this analysis to the galaxies and groups extracted from the Cosmicflows-3 catalog. We also use mock catalogs derived from numerical simulations to explore the effects of distance uncertainties on the derivation of the galaxy velocity flow onto groups. We determine the infalling velocity field onto galaxy groups with cz < 0.033 using peculiar velocity data. We measure the mean infall velocity onto group samples of different mass range, and also explore the impact of the environment where the group reside. Well beyond the group virial radius, the surrounding large-scale galaxy overdensity may impose additional infalling streaming amplitudes in the range 200 to 400 km s$^{-1}$. Also, we find that groups in samples with a well controlled galaxy density environment show an increasing infalling velocity amplitude with group mass, consistent with the predictions of the linear model. These results from observational data are in excellent agreement with those derived from the mock catalogs.
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