# Category:Congruence Modulo Subgroup

This category contains results about Congruence Modulo Subgroup.

Definitions specific to this category can be found in Definitions/Congruence Modulo Subgroup.

Let $G$ be a group.

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

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

### Left Congruence Modulo Subgroup

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

This is called **left congruence modulo $H$**.

### Right Congruence Modulo Subgroup

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

This is called **right congruence modulo $H$**.

## Pages in category "Congruence Modulo Subgroup"

The following 8 pages are in this category, out of 8 total.