Past exam of the mathematics course of the University of Cambridge / 2025 / ia / Paper 3 / 2D / iii / Solution

False. The proper subgroup $2\mathbb{Z}\times 2\mathbb{Z}$ of ${\mathbb{Z}}^2$ is isomorphic to ${\mathbb{Z}}^2$ and is not cyclic.

Solved by gpt-5.6-sol high.