We investigate the angular and kinematic distributions of satellite galaxies around a large sample of bright isolated primaries in the spectroscopic and photometric catalogues of the Sloan Digital Sky Survey (SDSS). We detect significant anisotropy in the spatial distribution of satellites. To test whether this anisotropy could be related to the rotating disks of satellites recently found by Ibata et al. in a sample of SDSS galaxies, we repeat and extend their analysis. Ibata et al. found an excess of satellites on opposite sides of their primaries having anticorrelated radial velocities. We find that this excess is sensitive to small changes in the sample selection criteria which can greatly reduce its significance. In addition, we find no evidence for correspondingly correlated velocities for satellites observed on the same side of their primaries, which would be expected for rotating disks of satellites. We conclude that the detection of coherent rotation in the satellite population in current observational samples is not robust. We compare our data to the $Lambda$CDM Millennium simulations populated with galaxies according to the semi-analytic model of Guo et al. We find excellent agreement with the spatial distribution of satellites in the SDSS data and the lack of a strong signal from coherent rotation.
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