Definition:Congruence Modulo Subgroup/Right Congruence/Also known as

Definition
Let $G$ be a group.

Let $H$ be a subgroup of $G$.

Let $\mathcal R^r_H$ be the relation of right congruence modulo $H$ (in $G$).

When $\tuple {x, y} \in \mathcal R^r_H$, we write:
 * $x \equiv^r y \pmod H$

which is read: $x$ is right congruent to $y$ modulo $H$.