The converse of Schur's theorem
Schur's theorem states that for a group \(G\) finiteness of the central factor-group implies the finiteness of the derived subgroup. The converse was proved by \textit{P. Hilton} [Int. J. Math. Math. Sci. 28, No. 8, 455-460 (2001; Zbl 1050.20021)] in case \(G/Z(G)\) is finitely generated. The author establishes that in such a case, \(|G/Z(G)|\leq |G'|^{d(G/Z(G))}\) and, provided the group \(G\) is nilpotent, \(|G/Z(G)|\) divides \(|G'|^{d(G/Z(G))}\).
scientific article; zbMATH DE number 5716890