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  "aliases": [
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  "body": "\n## Definition\n\nLet $G$ be a [[group|G5S1M9]] and let $g, h \\in G$.\nThe commutator of $g$ and $h$ is the element $[g, h] = g^{-1} h^{-1} g h$ of $G$.\n\n## Remarks\n\nThe equation $gh = hg [g, h]$ holds, so $[g, h] = e$ if and only if $gh = hg$.\nSome authors use the convention $[g, h] = g h g^{-1} h^{-1}$ instead.\nThe inverse of $[g, h]$ is $[h, g]$.\n\n## Explanations\n\n### L1 human\n\nThe commutator measures how far two elements are from commuting.\nIt is the correction factor that you need when you swap $g$ and $h$ in a product.\nIn an abelian group, every commutator is the identity.\n",
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