 Right coset

For a subgroup $H$ of a group $G$ and $g\in G$, its right coset is $Hg=\{hg:h\in H\}$. The map $h\mapsto hg$ is a bijection from $H$ onto $Hg$, with inverse $x\mapsto x{g}^{-1}$; in particular all right cosets have the same cardinality as $H$. Multiplication by subgroup elements is on the left in this expression because $g$ is the factor on the right.