On the relationships between the factors of the upper and lower central series in some non-periodic groups

This paper deals with the mutual relationships between the factor group G/ζ(G) (respectively G/ζk(G)) and G′ (respectively γk+1(G) and GN). It is proved that if G/ζ(G) (respectively G/ζk(G)) has finite 0-rank, then G′ (respectively γk+1(G) and GN) also have finite 0-rank. Furthermore, bounds for the 0-ranks of G′,γk+1(G) and GN are obtained.