Are compact groups of galaxies special?

It is often believed that isolated compact groups (CGs) of galaxies are special systems, but only a few studies have compared CGs to regular groups. We study the global properties and internal correlations of a volume- and luminosity-complete subsample of 78 groups of four members (CG4s) within the HMCG Hickson-like sample of compact groups. We compared these CGs to those of a similarly built subsample (including the three-magnitude range of CG4s) of the Lim regular groups. The latter were split into three control samples: one with the four brightest members (Control4Bs), one with the four closest members to the brightest group galaxy (BGG; Control4Cs), and one with exactly four members (RG4s). The vast majority of the CG4s are located within regular groups, and a large preponderance of the BGGs of these CG4s are the same as those of their host groups. The CG4s are smaller than the groups of all other samples and more luminous than RG4s. Both results are a consequence of their selection as high surface brightness systems. However, the CG4s (especially those split among several regular groups) have luminosities similar to Control4Cs. The CG4s also have higher velocity dispersions, probably because of a too-permissive redshift accordance criterion. The BGGs of the CG4s are not any more dominant in luminosity than those of RG4s, but they are significantly more offset relative to the group size because the Lim groups are built around their BGGs. In summary, compact groups have similar properties to regular groups of four galaxies and to the cores of regular groups once the selection criteria of CGs are considered. A large fraction of the CGs are the cores of regular groups, which are isolated on the sky by construction but rarely isolated in real space (from simulations), indicating that they are often plagued by chance alignments of host group galaxies along the line of sight.