\begin{definition}[Definition:Congruence Modulo Subgroup/Left Congruence/Also known as]
Let $G$ be a group.
Let $H$ be a subgroup of $G$.
Let $\RR^l_H$ be the relation of left congruence modulo $H$ (in $G$).
When $\tuple {x, y} \in \RR^l_H$, we write:
:$x \equiv^l y \pmod H$
which is read: '''$x$ is left congruent to $y$ modulo $H$'''.
\end{definition}