Definition:Congruence Modulo Subgroup/Right Congruence

Definition
Let $G$ be a group, and let $H$ be a subgroup of $G$. Then we can use $H$ to define a relation on $G$:


 * $\mathcal R^r_H = \set {\tuple {x, y} \in G \times G: x y^{-1} \in H}$

This is called right congruence modulo $H$.

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 $H$.

Also see

 * Definition:Left Congruence Modulo Subgroup


 * Right Congruence Modulo Subgroup is Equivalence Relation
 * Definition:Right Coset
 * Definition:Right Coset Space


 * Equivalent Statements for Congruence Modulo Subgroup