Editing Congruence relation (section)

=== Example: Groups ===
For example, a group is an algebraic object consisting of a [[set (mathematics)|set]] together with a single [[binary operation]], satisfying certain axioms.  If <math>G</math> is a group with operation <math>\ast</math>, a '''congruence relation''' on <math>G</math> is an equivalence relation <math>\equiv</math> on the elements of <math>G</math> satisfying
:<math>g_1 \equiv g_2 \ \ \,</math> and <math>\ \ \, h_1 \equiv h_2 \implies g_1 \ast h_1 \equiv g_2 \ast h_2</math> 
for all <math>g_1, g_2, h_1, h_2 \in G</math>. For a congruence on a group, the equivalence class containing the [[identity element]] is always a [[normal subgroup]], and the other equivalence classes are the other [[coset]]s of this subgroup.  Together, these equivalence classes are the elements of a [[quotient group]].