Coset of a subgroup (awaiting review)

If $G$ is a group and $H$ is a subgroup of $G$, then a left coset of $H$ is a set \[ gH = \{ gh \mid h \in H\} \] and similarly, a right coset of $H$ is a set \[ Hg = \{ hg \mid h \in H\}. \]

The left cosets partition $G$, as do the right cosets.