Right coset
= Right coset
{title2=$Hg$}
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 $x\mapsto xg^{-1}$; 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.