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  "body": "\n## Definition\n\nLet $G$ be a [[group|G5S1M9]], let $H$ be a [[subgroup|0X1JXT47GA]] of $G$, and let $g \\in G$.\nThe right coset of $H$ with representative $g$ is the set $Hg = \\{hg : h \\in H\\}$.\n\n## Remarks\n\nTwo right cosets $Ha$ and $Hb$ are equal when $ab^{-1} \\in H$, and they are disjoint otherwise.\nIn an [[abelian group|082GHNPJ53]], each right coset $Hg$ equals the [[left coset|03DEH43F4H]] $gH$.\nIn general $gH$ and $Hg$ can differ, but the map $gH \\mapsto Hg^{-1}$ is a bijection from the left cosets to the right cosets.\n\n## Explanations\n\n### L1 human\n\nA right coset is like a left coset, but you multiply the subgroup by the fixed element on the right.\nIn a group where the order of products matters, left and right cosets can be different sets.\nThe number of left cosets and the number of right cosets are always the same.\n",
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