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text: 'Let $G$ be a [-3gd] whose [3gg order] is equal to $p$, a [-4mf].\nThen $G$ is [49x isomorphic] to the [-47y] $C_p$ of order $p$.\n\n# Proof\nPick any non-identity element $g$ of the group.\n\nBy [4jn Lagrange's theorem], the subgroup generated by $g$ has size $1$ or $p$ (since $p$ was prime).\nBut it can't be $1$ because the only subgroup of size $1$ is the trivial subgroup.\n\nHence the subgroup must be the entire group.',
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