Is $\mathbb{Z}\times G$ Hopfian where $G$ is a finite group?

Question

Recall that a group ‎$‎G‎$‎ is Hopfian if every epimorphism ‎$‎f :G\to G‎$‎ is an automorphism. We know that finitely generated residually finite groups and free groups of finite rank are Hopfian. Now assume that $G$ is a finite group. Is $\mathbb{Z}\times G$ Hopfian?

Answer 1

$\mathbb{Z}$ is residually finite, of course. Finite groups are also residually finite, trivially. Both are finitely generated.

Furthermore the product of two finitely generated groups is finitely generated. And the product of two residually finite groups is residually finite. This proves that $\mathbb{Z}\times G$ is a finitely generated residually finite group, and thus Hopfian.

Answer 2

In this 1969 AMS paper "Some Theorems on Hopficity", by R. Hirshon, it is shown that a direct product of a finitely generated Hopfian group with a finite group is Hopfian.