Finitely generated residually torsion-free nilpotent groups. I

Gilbert Baumslag
1999 Journal of the Australian Mathematical Society  
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 Mathematics
more » ... ct classification (Amer. Math. Soc): primary 20F18.
doi:10.1017/s1446788700002032 fatcat:cun3u2fvvbgolg2ptbmg6bfgd4