Solution
= Solution
{c}
Let $|G|=p$, with $p$ a <prime number>, and choose $g\ne e$. By <Lagrange's theorem>, the <order of a group element> $g$ divides $p$ and is greater than one. It is therefore $p$, and $G=\langle g\rangle$. Hence \b[a <group> of prime <cardinality> is a <cyclic group>].
The converse is false: the <cyclic group> $C_4$ has four elements, and $4$ is not a <prime number>.