The genus of a direct product of certain nilpotent groups with a finite nilpotent group (Q1924587)

Hilton and Mislin showed that the genus \({\mathcal G}(N)\) of a finitely generated infinite nilpotent group \(N\) with a finite commutator subgroup has the structure of a finite abelian group. In this paper the techniques developed by Hilton on induced morphisms of genera are used to study the genus of a direct product of a finite nilpotent group \(M\) and a finitely generated infinite nilpotent group \(N\) with finite commutator subgroup. It is shown that \({\mathcal G}(N\times M)\cong{\mathcal G}(N)\).