Past exam of the mathematics course of the year 2 of the natural sciences course of the University of Cambridge / 2024 / Paper 2 / 8 / d / Solution

Choose $g\ne e$ in a group of prime group order $p$. Its order of a group element divides $p$ by (c) and is not $1$, hence equals $p$. Consequently its cyclic subgroup already contains all elements of $G$:Thus every nonidentity element is a group generator.