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The object of this paper is to study the sequence of torsion-free ranks of the quotients by the terms of the lower central series of a finitely generated group. This gives rise to the introduction into the study of finitely generated, residually torsion-free nilpotent groups of notions relating to the Gelfand-Kirillov dimension. These notions are explored here. The main result concerning the sequences alluded to is the proof that there are continuously many such sequences. 1991 Mathematicsdoi:10.1017/s1446788700002032 fatcat:cun3u2fvvbgolg2ptbmg6bfgd4