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

Definition

Let $G$ be a group.

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

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

When $\tuple {x, y} \in \mathcal R^l_H$, we write:

$x \equiv^l y \pmod H$

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