Aims. We use accurate data on distances and radial velocities of galaxies around the Local Group, as well as around 14 other massive nearby groups, to estimate their radius of the zero-velocity surface, R _(0) , which separates any group against the global cosmic expansion. Methods. Our R _(0) estimate was based on fitting the data to the velocity field expected from the spherical infall model, including effects of the cosmological constant. The reported uncertainties were derived by a Monte Carlo simulation. Results. Testing various assumptions about a location of the group barycentre, we found the optimal estimates of the radius to be 0.91 ± 0.05 Mpc for the Local Group, and 0.93 ± 0.02 Mpc for a synthetic group stacked from 14 other groups in the Local Volume. Under the standard Planck model parameters, these quantities correspond to the total mass of the group ~ (1.6 ± 0.2) × 10~(12) M _(⊙) . Thus, we are faced with the paradoxical result that the total mass estimate on the scale of R _(0)≈ (3?4) R _(vir) is only 60 % of the virial mass estimate. Anyway, we conclude that wide outskirts of the nearby groups do not contain a large amount of hidden mass outside their virial radius.
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