Groups of galaxies in the SDSS Data Release 5. A group-finder and a catalogue

We extract groups of galaxies from the SDSS Data Release 5 with the purpose of studying the supercluster-void network and environmental properties of groups therein. We use a modified friends-of-friends (FoF) method with adopted variable linking length in transverse and radial direction to eliminate selection effects and to find reliably as many groups as possible to track the supercluster network. We take into account various selection effects due to the use of a magnitude limited sample. To determine linking length scaling we study the luminosity-density relation in observed groups. We follow the changes in group sizes and mean galaxy number densities within groups when shifting nearby groups to larger distances. As a result we show that the linking length should be a slowly growing function with distance. Our final sample contains 17143 groups in the equatorial, and 33219 groups in the northern part of the DR5 survey with membership N_g >= 2. The group catalogue is available at our web-site http://www.obs.ee/~erik/index.html. Due to a narrow magnitude window in the SDSS the group catalogue based on this survey has been obtained by moderately growing linking length scaling law up to redshift z = 0.12. Above this redshift the scaling law turns down. In the redshift range z=0.12 - 0.2 only the cores are detected. Along with applying weights when calculating luminosities it is possible to use groups for determination of the large-scale luminosity-density field.