Definition:Congruence Modulo Subgroup

Definition
Let $G$ be a group.

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

We can use $H$ to define relations on $G$ as follows:

Also see

 * Equivalent Statements for Congruence Modulo Subgroup


 * Congruence Modulo Subgroup is Equivalence Relation


 * Definition:Coset
 * Definition:Coset Space