\begin{definition}[Definition:Congruence Modulo Subgroup/Right Congruence]
Let $G$ be a group.
Let $H$ be a subgroup of $G$.
We can use $H$ to define a relation on $G$ as follows:
:$\RR^r_H = \set {\tuple {x, y} \in G \times G: x y^{-1} \in H}$
This is called '''right congruence modulo $H$'''.
\end{definition}