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  "body": "\n## Example\n\nLet $p \u003c q$ be prime numbers such that $p$ does not divide $q - 1$, and let $G$ be a group of order $pq$.\nThe number $n_q$ divides $p$ and satisfies $n_q \\equiv 1 \\pmod q$, so $n_q = 1$, because $p \u003c q$.\nThe number $n_p$ divides $q$ and satisfies $n_p \\equiv 1 \\pmod p$; since $p \\nmid q - 1$, $n_p = 1$.\nSo $G$ has a [[normal|0CB0DX5BVV]] subgroup $P$ of order $p$ and a normal subgroup $Q$ of order $q$.\nThey meet only in $e$, so $G$ is the [[internal direct product|0VBZH90R1A]] of $P$ and $Q$.\nThus $G \\cong \\mathbb{Z}/p\\mathbb{Z} \\times \\mathbb{Z}/q\\mathbb{Z} \\cong \\mathbb{Z}/pq\\mathbb{Z}$, and $G$ is cyclic.\nFor example, each group of order $15$ is cyclic.\nIf $p$ divides $q - 1$, there is also a group of order $pq$ that is not cyclic, for example the dihedral group $D_3$ of order $6$.\n",
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