Peyman Niroomand
Arch. Math(Basel) - 94, 5, 401-403 - January, 2010 - .
Publication year: 2010


Schur’s theorem states that for a group G finiteness of G/Z(G) implies the finiteness of G′. In this paper, we show the converse is true provided that G/Z(G) is finitely generated and in such case, we have |G/Z(G)| ≤ |G′| d(G/Z(G)). In the special case of Gbeing nilpotent, we prove |G/Z(G)| divides |G′| d(G/Z(G)).