The two-point correlation function is computed for galaxies and groups of galaxies selected using 3-dimensional information from the Updated Zwicky Galaxy Catalog - ( UZC ) .
The redshift space distortion of the correlation function \xi ( \sigma, \pi ) in the directions parallel and perpendicular to the line of sight , induced by pairwise group peculiar velocities is evaluated .

Two methods are used to characterize the pairwise velocity field of groups and galaxies .
The first method consists in fitting the observed \xi ( \sigma, \pi ) with a distorted model of an exponential 1-dimensional pairwise velocity distribution , in fixed \sigma bins .
The second method compares the contours of constant predicted correlation function of this model with the data .
The results are consistent with a 1-dimensional pairwise rms velocity dispersion of groups < w ^ { 2 } > ^ { 1 / 2 } = 250 \pm 110 km s ^ { -1 } .
We find that UZC galaxy 1-dimensional pairwise rms velocity dispersion is < w ^ { 2 } > ^ { 1 / 2 } = 460 \pm 35 km s ^ { -1 } .
Such findings point towards a smoothly varying peculiar velocity field from galaxies to systems of galaxies , as expected in a hierarchical scenario of structure formation .

We find that the real-space correlation functions of galaxies and groups in UZC can be well approximated by power laws of the form \xi ( r ) = ( r / r _ { 0 } ) ^ { \gamma } .
The values of \gamma for each case are derived from the correlation function in projected separations \omega ( \sigma ) .
Using these estimates we obtain r _ { 0 } from the projected correlation functions .
The best fitting parameters are \gamma = -1.89 \pm 0.17 and r _ { 0 } = 9.7 \pm 4.5 h ^ { -1 } Mpc for groups , and \gamma = -2.00 \pm 0.03 and r _ { 0 } = 5.29 \pm 0.21 h ^ { -1 } Mpc for galaxies .

The \beta -parameter ( \beta = \Omega ^ { 0.6 } / b ) is estimated for groups and galaxies using the linear approximation regime relating real and redshift-space correlation functions .
We find \beta _ { gx } = 0.51 \pm 0.15 for galaxies , in agreement with previous works , while for groups we obtain a noisy estimate \beta < 1.5 .

Both methods used to characterize the pairwise velocity field are also tested on mock catalogs taken from CDM numerical simulations .
The results show that the conclusions derived from the application of both methods to the observations are reliable .
We also find that the second method , developed in this paper , provides more stable and precise results .