Definition:Congruence Modulo Subgroup/Right Congruence

Definition
Let $G$ be a group.

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

Then we can use $H$ to define a relation on $G$ as follows:


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

This is called right congruence modulo $H$.

Also see

 * Equivalence of Definitions of Right Congruence Modulo Subgroup


 * 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