$\boxed{\mathbb Z^4\text{ is not a nontrivial free product}.}$ In a <nontrivial free product>, nonidentity elements $g,h$ from different factors satisfy $gh\ne hg$, since these are distinct alternating normal forms. Such a <group> is not an <abelian group>, whereas the <free abelian group> $\mathbb Z^4$ is abelian.

Solution

Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 104 / 1 / ii / Solution

 Solution (source code)