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  "body": "\n## Statement\n\nLet $n \\geq 2$.\nThe [[symmetric group|0515A6D2Y1]] $S_n$ is [[generated|0RP7VWQ0YN]] by its [[transpositions|0FWVRHBRWM]].\n\n## Remarks\n\nThis is a reformulation of the [[decomposition into transpositions|0XK6FECMW5]].\nThe adjacent transpositions $(1\\ 2), (2\\ 3), \\dots, (n-1\\ n)$ already generate $S_n$.\nThe two elements $(1\\ 2)$ and $(1\\ 2\\ \\dots\\ n)$ also generate $S_n$.\n\n## Explanations\n\n### L1 human\n\nEach permutation is a product of swaps, so the swaps generate the whole symmetric group.\nYou do not even need all swaps.\nSwaps of neighbours are enough, as in a bubble sort.\n",
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