Category:Definitions/Congruence Modulo Subgroup

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This category contains definitions related to Congruence Modulo Subgroup.
Related results can be found in Category: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 $H$.