We have carried out multicolour imaging of a complete sample of radio-loud quasars at 0.6 < z < 1.1 and find groups or clusters of galaxies in the fields of at least 8 and possibly 13 of the 21 sources. There is no evidence for an evolution in the richness of the environments of radio-loud quasars from other low-redshift studies to z >~ 0.9. The quasars associated with groups and clusters in our sample do not necessarily reside in the centre of the galaxy distribution which rarely displays a spherical geometry. Clustering is preferentially associated with small or asymmetric steep-spectrum radio sources. The quasars with the largest projected angular size are, in nearly all cases, found in non-clustered environments. Radio-based selection (including source size) of high-redshift groups and clusters can be a very efficient method of detecting rich environments at these redshifts. We find that in optical searches for galaxy overdensities above z ~ 0.6 multiple filters must be used. If the single-filter counting statistics used by groups at lower redshift are applied to our data, uncertainties are too large to make accurate quantifications of cluster richness. This means that genuine clustering of galaxies about quasars will be missed and, in ~10% of cases, putative clusters turn out to be false detections. The statistics are further diluted by the fact that galaxy overdensities are generally not centred on the quasar.
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