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  "body": "\n## Summary\n\nLet $G$ be a [[group|G5S1M9]], $H$ a [[subgroup|0X1JXT47GA]] and $S$ a set of elements of $G$.\nThe Schreier coset graph is a [[directed graph|0KFYGSHHF5]] whose vertices are the [[right cosets|0NE1DK7H4T]] of $H$, with an edge labelled $s$ from $Hg$ to $Hgs$.\nFor $H = \\set{1}$ it is the [[Cayley graph|0GYQK9NDJF]] of $G$ with respect to $S$.\nIt shows how the generators permute the cosets of $H$.\nIt is used in coset enumeration and to find generators of subgroups, as in the Reidemeister–Schreier method.\n\n## Explanations\n\n### L1 human\n\nGroup the elements of $G$ into the right cosets of $H$, and draw one dot for each coset.\nEach generator $s$ moves a coset $Hg$ to the coset $Hgs$; draw an arrow for this move.\nFor example, in $\\Z$ with $H = 3\\Z$ and the generator $1$, there are three dots $3\\Z$, $1 + 3\\Z$ and $2 + 3\\Z$, and the arrows form a triangle.\nPaths in the graph that start and end at the dot $H$ spell words that represent elements of $H$.\n",
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