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

Abstract

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 G ). It is proved that if G/ζ(G) (respectively G/ζk(G)) has finite 0-rank, then G ′ (respectively γk+1(G) and G ) also have finite 0-rank. Furthermore, bounds for the 0-ranks of G′, γk+1(G) and G N are obtained.