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  "body": "\n## Example\n\nLet $S_3$ be the [[symmetric group|0515A6D2Y1]] on $\\{1, 2, 3\\}$. Compose permutations from right to left.\nTake the [[transpositions|02DTRYKGE8]] $(1\\,2)$ and $(1\\,3)$.\nThen $(1\\,2)(1\\,3) = (1\\,3\\,2)$ and $(1\\,3)(1\\,2) = (1\\,2\\,3)$.\nThese two products are different. Thus $S_3$ is not [[abelian|071DDFVG4J]].\n\n## Remarks\n\n$S_3$ has $6$ elements. It is the smallest group that is not abelian.\n",
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