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  "body": "\n## Proof\n\n1. Let $G$ be a [[cyclic group|0B85Q41RP6]] with generator $g$.\n2. Let $x$ and $y$ be elements of $G$. Then there are integers $m$ and $n$ with $x = g^m$ and $y = g^n$.\n3. By the [[laws of exponents|00DRK90Z6K]], $xy = g^m g^n = g^{m+n}$.\n4. In the same way, $yx = g^n g^m = g^{n+m}$.\n5. Since $m + n = n + m$, $xy = yx$. Thus $G$ is [[abelian|071DDFVG4J]].\n\n## Idea\n\nEvery element is a power of one generator, and powers of the same element commute.\n",
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