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  "body": "\n## Example\n\nLet $G = (\\mathbb{Z}, +)$ be the [[integers|0C4JS9RF5M]] with addition, and let $O$ be the set of odd integers.\nThe identity $0$ is not odd, so $0 \\notin O$.\nAlso, $1 \\in O$ and $1 + 1 = 2 \\notin O$. Thus $O$ is not closed under addition.\nThus $O$ is not a [[subgroup|0N0PXCTYA7]] of $G$.\n\n## Remarks\n\n$O$ is a coset of the even integers. A coset $g + H$ is a subgroup only when $g \\in H$.\n",
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        "url": "https://en.wikipedia.org/wiki/Subgroup"
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        "locator": "Even and odd integers",
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