{
  "aliases": [
    "co-set",
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  "body": "\n## Summary\n\nIn mathematics, specifically group theory, a [[subgroup|0X1JXT47GA]] $H$ of a group $G$ may be used to decompose the underlying [[set|0BSJ7RQ9BW]] of $G$ into [[disjoint|0W4RPA8QH3]], equal-size [[subsets|0BJR9QR08E]] called **cosets**. There are *left cosets* and *right cosets*. Cosets (both left and right) have the same number of elements ([[cardinality|0G0ASKNA6Z]]) as does $H$. Furthermore, $H$ itself is both a left coset and a right coset. The number of left cosets of $H$ in $G$ is equal to the number of right cosets of $H$ in $G$. This common value is called the [[index|0DTXBQPA2S]] of $H$ in $G$ and is usually denoted by $[G : H]$.\n",
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  "name": "Coset",
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