Abstract
groups of the lower central series of classes of nonfree groups and to find formulas for their ranks analogous to (1 .l). In this paper we continue the work of Dark [l], Struik [15, 161, and Waldinger [17, 181 by studying the lower central series of groups, G, that are free products of finitely generated Abelian groups. Our groups, G, are in general not residually nilpotent and are in a sense diametrically opposite to the residually nilpotent groups investigated in [14]. By the use of Philip Hall’s “collection process” [5, 71 and Marshall Hall’s “basic commutators” [4, 51, we obtain our first result:
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