Drawbacks of the Criteria Used to Identify Isolated Galaxies

Using the volume-limited main galaxy sample of the Sloan Digital Sky Survey Data Release 6 (SDSS DR6), we explore drawbacks of the selection criteria of isolated galaxies developed by Karachentseva, published in 1973. We find that about 35.36% of the isolated galaxies identified by Karachentseva's main criterion x(i,j) >= 20 x a(j) lie in groups or clusters, which may lead to the result that there are no significant statistical differences of galaxy properties between group and cluster galaxies and isolated galaxies. Our work at least suggests that searches for better methods to find isolated galaxies are needed.