Correlation function of galaxy groups

We use the Updated Zwicky Catalog of galaxies to generate a catalog of grou ps by means of a friends-of-friends algorithm. The groups identified have f our or more members and a surrounding density contrast delta rho/rho = 80. They cover the region -4 degrees < <delta> < 90<degrees>, \b\ > 20 degrees spanning the radial velocity range of 2000 < cz < 15,000 km s(-1). The tota l sample (hereafter GUZC) comprises 517 groups. The correlation length of t he total sample is well fitted with a power law xi>(*) over bar * (r) = (r/ r(0))(gamma), with parameters r(0) = 9.0 +/- 0.4 h(-1) Mpc and gamma = -1.6 7 +/- 0.09 for values of r < 70 h(-1) Mpc, declining to homogeneity at larg er scales. Three subsamples defined by the range of group virial masses M w ere used to examine their clustering properties throughout the autocorrelat ion function. We find an increase of the amplitude of the correlation funct ion according to the group masses, which extends the results of the r(0)-d( c) relation for galaxy systems at small d(c). We obtain r(0) = 9.5 +/- 0.5 h(-1) Mpc (<gamma> = -1.81 +/- 0.12), r(0) = 10.8 +/- 0.7 h(-1) Mpc (gamma = -1.77 +/- 0.17), and r(0) = 14.1 +/- 1.2 h(-1) Mpc (gamma = -1.65 +/- 0.2 2) for mass ranges 5 x 10(12) < M < 4 x 10(14) M., 2 x 10(13) < M < 4 x 10( 14) M., and 5 x 10(13) < M 4 x 10(14) M., respectively. For completeness, w e have also analyzed a sample of groups obtained from the Southern Sky Reds hift Survey in the range of virial masses 5 x 10(12) < M < 4 x 10(14) M. to compare the results with those obtained from GUZC. The correlation functio n of this sample can be fitted with a power law with parameters r(0) = 8.4 +/- 1.8 h(-1) Mpc and <gamma> = -2.0 +/- 0.7.