Left coset
= Left coset
{title2=$gH$}
For a <subgroup> $H$ of a <group> $G$ and $g\in G$, its left coset is $gH=\{gh:h\in H\}$. Left multiplication $h\mapsto gh$ is a <bijection> from $H$ onto $gH$. Left and <right cosets> agree for every $g$ exactly when $H$ is a <normal subgroup>.