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  "body": "\n## Example\n\nLet $G = (\\mathbb{Z}, +)$ be the [[integers|0C4JS9RF5M]] with addition, and let $2\\mathbb{Z}$ be the set of even integers.\nThe identity $0$ is even.\nThe sum of two even integers is even, and the negative of an even integer is even.\nThus $2\\mathbb{Z}$ is a [[subgroup|0N0PXCTYA7]] of $G$.\n$G$ is abelian, so $g + 2\\mathbb{Z} = 2\\mathbb{Z} + g$ for each $g$. Thus $2\\mathbb{Z}$ is [[normal|0W77CVBCHQ]] in $G$.\n\n## Remarks\n\nIn the same way, $n\\mathbb{Z}$ is a subgroup of $\\mathbb{Z}$ for each $n \\ge 0$.\n",
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